∗ 106 /25 −50 ∗ 103 ) = 88 thousandshares
Day 3 setting of € 10
0.8
Buy delta times 9 ∗ 106 dividedby the average 3 day shareprice minus the sharesbought on the first two days,(0.8 ∗ 9 ∗ 106 /20 − 116 ∗103 ) = 222 thousand shares
Number of sharesbought as a hedge
first two days, he has to buy another 222 thousand shares of BMWon the day of the last Asian in setting to be fully hedged. A summaryof the hedging process for this Asian in put option can be found inTable 18.1.
18.6 ASIAN IN FORWARDThe Asian in forward is a very popular structure and is often used bycorporates to buy back their own stock. An Asian in forward is composed of a long Asian in call and a short Asian in put, both of whichhave the same observation dates serving as Asian in settings and bothexpire on the last Asian in setting. In other words, the Asian in forward expires on the very same day that the strike is set according tothe Asian in schedule. This means that, if BMW wants to repurchase€ 900 million worth of its own stock over the next 30 days, it couldexecute this by buying a 30 day Asian in call and selling a 30 dayAsian in put, where each Asian in setting has the same weight, 1/30.
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Executing this stock repurchase through an Asian in forward, ratherthan buying the stock back in the market place, bears a significantadvantage for BMW. This is because there is hidden gamma embedded in the Asian in forward. The investment bank that facilitates thisAsian in forward and is therefore buying the Asian in put and selling the Asian in call, can easily monetise this gamma. The embeddedgamma in this Asian in forward makes it an incredibly powerful structure and a very attractive solution to any corporate that wants to repurchase its own stock. The following example shows that an investmentbank does actually materialise a gain on the gamma within the Asianin forward.Suppose that BMW uses an Asian in forward to repurchase its ownstock, where each Asian in setting has the same weight. For the sake ofclarity it is assumed that BMW wants to buy back € 900 million worthof stock in three days rather than 30 days. BMW stock has the followingprice trend over the 3 days of the Asian in term:1. € 302. € 203. € 10Since BMW wants to buy € 900 million worth of stock at the average3 day stock price, BMW expects to get delivered 45 million shares ofBMW on day 3 and pays € 20 for each share. This means that on thethird day BMW pays the investment bank € 900 million and in returnthe investment bank delivers 45 million of BMW’s own shares. Sincethe delta of the Asian in forward will be 1 on the day of the last Asianin setting, i.e. the day the strike price is set, the investment bank needsto make sure that it buys € 900 million worth of stock over the threeday Asian in term. This € 900 million worth of BMW stock is determined on the basis of a BMW share price that is equal to the 3 dayaverage BMW price. In other words the investment bank needs to havea hedging scheme that makes sure it has accumulated 45 million stockon the third day. This hedging scheme along with its economic implications can be summarised by Table 18.2. The table makes clear that theinvestment bank does actually make money on the gamma embeddedin the Asian in forward, as the hedging scheme accumulates 45 million shares over the course of three days, for which the investment bankonly pays € 780 million, after which it sells these 45 million shares for€ 900 million to BMW itself. Thus, the fact that the share price movesaccording to the prescribed price trend ensures that the investment bank
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Table 18.2 Hedging the Asian in forwardBMW share price foreach Asian setting
Number of sharesbought as a hedge
Total cost of the hedgeon each Asian setting day
Day 1 setting of € 30
Buy a third of 900 divided bythe average 1 day share price,1/3 ∗ 900/30 = 10 millionsharesBuy 1/2 of 900 divided by theaverage 2 day share priceminus the shares bought onthe first day,1/2 ∗ (900/25 − 10) = 13million sharesBuy 900 divided by the average3 day share price minus theshares bought on the first twodays, (900/20 − 23) = 22million shares
€ 300 million
Day 2 setting of € 20
Day 3 setting of € 10
€ 260 million
€ 220 million
makes a profit of € 120 million. Since the Asian in forward fixes thenotional rather than the number of shares, the number of shares to bedelivered on the day of the last Asian setting is dependent on the average share price over the Asian in period. Since the average goes upif the share price goes up, the investment bank buys fewer shares ona day that the share price goes up and more shares on a day that theshare price goes down. This effectively means that the investment bankbuys shares low and sells them high, which is exactly the definitionof being long gamma. The investment bank will obviously compensateBMW for the fact that the Asian in forward gives the investment bankthe opportunity to be long gamma and will therefore pay BMW a better price for the Asian in forward. Obviously, the higher the volatilityof BMW the more the investment bank will pay BMW for this Asianin forward.
18.7 PRICING THE ASIAN IN FORWARDPricing the Asian in forward is relatively benign and is typically done bya Monte Carlo process where the main input is the volatility. Although aMonte Carlo process can easily provide a price for the Asian in forward,
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this sub-section discusses the pricing from an economical perspectiveand will therefore provide a better insight into the dynamics of the Asianin forward. Sub-section 18.6 showed that the volatility of the underlyingstrongly affects the price of the Asian in forward. The higher the underlying volatility the more an investment bank is prepared to pay for beinglong the Asian in put and short the Asian in call. However, to recognise another very important aspect that affects the price of the Asian inforward, it is assumed that the volatility of the underlying is zero. Inthis case the underlying price stays the same throughout the term of theAsian in period and therefore the delta hedge that is executed on eachday is known upfront and the same is true for all Asian in settings. In thiscase the price of the Asian in forward is very easy to determine. Namely,the investment bank will only charge the corporate for the financing ofthe delta hedge, because the investment bank will pay money on eachof the Asian setting days to purchase the shares but will only receive themoney from the corporate on the day of the last Asian in setting. Thisbasically means that the investment bank will lose interest over the termof the Asian in settings and will charge that through to the corporate. Toquantify this better, consider the example where BMW wants to repurchase € 900 million of its own stock through a 30 day Asian in forward.Since the volatility is assumed to be zero, the investment bank will hedgeitself on each day of an Asian in setting by buying € 30 million worthof stock. This means that the investment bank will lose interest for 29days on the first € 30 million plus for 28 days on the second € 30 million plus . . . plus for 1 day on the penultimate € 30 million. Obviouslyone can calculate the exact cost of this financing, but an easier methodis to say that the investment bank incurs financing for 29 days on halfthe full notional, i.e. € 450 million. Assuming that the euro interest rateis 0.03 per annum, one calculates that the investment bank will chargeBMW € 450 ∗ 0.03 ∗ 29/365 = 1.0875 million, which is equivalent to1/2 ∗ 0.03 ∗ 29/365 = 0.1192 % of the full notional of € 900 million.Obviously, since BMW’s share price does move, the investment bank,depending on the volatility, might end up paying BMW for the Asianin forward, as the structure makes the investment bank long gamma.This effect can also be estimated when one knows the gamma on theAsian in forward and by using the profit formula described in equation2.3. Since the gamma is not constant this estimate will not be accurate and hence a Monte Carlo process is needed to calculate the exactprice.
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18.8 ASIAN IN FORWARD WITH OPTIONALEARLY TERMINATIONThe last interesting class of Asian option structures is the Asian in forward with a clause that the buyer of the Asian in put, and therefore theseller of the Asian in call, has the option to terminate early the Asian inforward. In other words, the investment bank has the option to deliverthe shares early at the average share price up to the early terminationday. The reason that this is such a popular structure is that it gives theinvestment bank additional optionality and therefore the corporate whois looking to repurchase stock takes advantage of yet another gammafeature that enhances the premium the corporate receives for buyingback stock. There are two ways of pricing this Asian in forward withoptional early termination. One can either price this is as a Monte Carloprocess or one can estimate the price by pricing the regular Asian inforward and adding the price of an Asian in put to this. Although thelatter method will not give the exact price for the Asian in forward withearly termination, it is very useful in getting an intuitive feel for thestructure and what affects its price. Therefore this sub-section will firstdiscuss how to accurately estimate the price of the Asian in forwardwith early termination, after which it will discuss the exact pricing ofthe Asian in forward with optional early termination through the MonteCarlo method.Consider a 33 day Asian in forward on BMW on a notional of € 900million. The buyer of the Asian in put, and therefore the seller of theAsian in call, has the option to deliver € 900 million worth of BMWshares early at any day after day 29, i.e. either day 30, 31 or day 32,at the average share price up to that point. The investment bank wouldobviously only choose to early terminate if the close on any of the 30th,31st or 32nd days is lower than the average over respectively the first30, 31 or 32 days. This means that, if the investment bank wants to earlyterminate on the 30th day, it will buy all the remaining shares to beable to deliver € 900 million worth of stock at the average of the first30 days. Since the investment bank has the option to early terminateand would only do that if the close on the 30th day is lower than theaverage of the preceding 30 days, the investment bank is basically longa 30 day Asian in put that expires on day 30. By exercising this Asianin put, the investment bank must buy back the remaining shares thatwould otherwise have been bought over the next 3 days. This means thatthe notional on this put should be 3/33 times the notional on the full
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Asian in forward. Since the investment bank can also decide to earlyterminate on the 31st or 32nd day, a lower estimate for the price of the33 day Asian in forward with optional early termination from day 30 isto price it as a 30 day Asian in forward on 30/33 times € 900 millionplus a 30 day Asian in put on 3/33 times € 900 million. Armed withthis intuition one can more easily understand how to price the Asian inforward with optional early termination as a Monte Carlo process.When pricing the Asian in forward with optional early terminationas a Monte Carlo process, it is important to realise that this is a MonteCarlo process with certain conditions. As observed previously, the investment bank which is short the Asian in forward (long Asian in putand short Asian in call) would early terminate on any of the days inthe early termination period if the prevailing stock price divided by theaverage stock price up to that point was less than a certain constant.This constant will always be less than 1, but to get the right price for theAsian in forward with optional early termination, one has to optimisethis constant7 for each day in the early termination period, i.e. in theexample above one would need to optimise these constants for the 30th,31st and 32nd days. The process of optimising these constants worksalong the same lines as optimising the barriers for the callable reverseconvertible, see sub-section 17.1. One starts backwards and optimisesthe constant for the last day while keeping the constants for the previousdays at zero to make sure that the structure has not been early terminated. Subsequently, one works backwards to optimise the constant forthe preceding days. Once these constants on each day in the early termination period have been established by using the Newton–Raphsonmethod, one prices the Asian in forward with optional early termination as the following Monte Carlo process. Suppose that the optimisedconstants are C0 , C1 and C2 for respectively the 30th, 31st and 32ndday.
r For all paths where
S3030 Sii=1 30
≤ C0 the Monte Carlo process prices a
30 day Asian in forward on 30/33 of € 900 million and a 30 dayAsian in put on 3/33 of € 900 million.r For all paths where 30S30 S > C0 and 31S31 S ≤ C1 the Monte Carloiii=1 30
i=1 31
process prices a 31 day Asian in forward on 31/33 of € 900 millionand a 31 day Asian in put on 2/33 of € 900 million.7Note that this is a conservative estimate as it does not need to be a constant but can be any number associatedto any Monte Carlo path which optimises the price of the Asian in forward.
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r For all paths where
S3030 Sii=1 30
> C0 and
S3131 Sii=1 31
> C1 and
S3232 Sii=1 32
≤ C2
the Monte Carlo process prices a 32 day Asian in forward on 32/33of € 900 million and a 32 day Asian in put on 1/33 of € 900 million.r For all paths where 30S30 S > C0 and 31S31 S > C1 and 32S32 S > C2iiii=1 30
i=1 31
i=1 32
the Monte Carlo process prices a 33 day Asian in forward on € 900million.
19Quanto Options1The quanto option is designed for investors who want to execute anoption strategy on a foreign stock but are only interested in the percentagereturn of that strategy and want to get paid this return in their owncurrency. The basic principle of a quanto option is that the exchange ratewill be fixed to the prevailing exchange rate at inception of the optiontransaction and the payout of the quanto option will be this exchangerate times the payout of the regular option.Consider a US investor who is very bullish on the share price of BP(British Petroleum). For that reason this US investor wants to buy anATM call option on BP expiring in one year. However, he does not wantto get his return in British pounds but in US dollars. Assume that BP’sshare price is £ 5, the exchange rate is currently 2 dollars per pound andin one year’s time the share price is worth £ 5.50. The quanto ATM calloption will give the US investor a payout at maturity of $ 1 regardless ofthe change in exchange rate. In other words, the investor would expect a10 % return in US dollars on the USD notional2 amount he bought callson, since BP’s share price has increased by 10 %.From the above example it is clear that it is relatively easy to structurea quanto option, however it is much harder to see what effect it has onhow this option should be priced and what variables it depends on.
19.1 PRICING AND CORRELATION RISK OFTHE QUANTO OPTIONTo see how the quanto option should be priced, two new variables haveto be introduced. The first variable is the correlation between BP’s stockprice and the foreign exchange, FX, rate. To get a better understandingof how this correlation affects the price of a quanto call option, an interesting question is whether the US investor, who is buying an ATMUSD quanto call, is short or long correlation. Here short correlation1Parts of this chapter have been previously published in de Weert, F. (2006) An Introduction to OptionsTrading, John Wiley & Sons Ltd, Chichester. Reproduced with permission.2Notional is defined as the number of options times the strike price.
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means that the investor benefits (quanto option increases in value) ifthe correlation goes down and loses if the correlation goes up. Thereverse holds for being long correlation. To answer this question, assume the correlation is positive, which means that, if the British poundgets more valuable against the US dollar, BP’s share price goes up.Now, one can easily see that the investor is short correlation (sellingcorrelation). Because, if the British pound goes up, the correlation aspect causes the share price to go up and therefore the dollar increaseof a plain vanilla call option, which is effectively a quanto option withzero correlation, is more than the dollar increase of the USD quantocall option, which has a fixed exchange rate. A similar analysis showsthat, if the British pound goes down, the correlation aspect causes theshare price to go down and the combination of a lower share price anda less valuable pound causes the dollar loss of a plain vanilla ATMcall option to be less than the dollar loss of an ATM USD quanto calloption. To put it differently, if the correlation goes down from for example 1 to −1, the holder of a USD quanto call option benefits, sincehe is better off holding a plain vanilla call3 option if the correlationis 1 whereas if the correlation is −1 he is better off holding a USDquanto call option. The above example shows that the holder of a USDquanto call is short correlation. However, when extending this analysisto a USD quanto put one finds that the holder of such an option is longcorrelation.The second variable is the FX volatility. For this variable it is lessobvious whether the US investor is long or short this FX volatility. Atthis point it is good to introduce a model that describes the stock pricedifference in US dollars for a small time interval. This model gives ananswer under which circumstances a quanto option is long or short FXvolatility and shows once more why the holder of a quanto call is shortcorrelation and the holder of a quanto put is long correlation.The model most commonly used for modeling a share price on a nondividend paying stock is the Black–Scholes model which describes thedifference in stock price for a small time interval. The formula is asfollows.d St= r dt + σ S d Wt ,(19.1)St3A plain vanilla option is equivalent to a quanto option where the correlation between the exchange rate andthe stock price is zero. The only difference is that the quanto option is priced in the quanto currency and the plainvanilla option in the share’s own currency. This means that to have an exact comparison one should have the FXtimes as many quanto options as regular options.
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where
r St is the stock price at time t.r r is the risk free interest rate.r d St is the change in stock price over time interval dt.r dt is a small time interval.r σ S is the volatility of the stock price.r Wt is Brownian motion, which is a stochastic process characterised bynormally distributed intervals dt with a mean of 0 and a variance equalto the length of the interval dt. Mathematically stated the intervals dthave a distribution equal to N (0, dt).r d Wt is a stochastic process with distribution N (0, dt).For the purpose of understanding a quanto option, a similar modelto equation 19.1 is required which includes two additional variables,namely the correlation, ρ, between the logarithm of the stock price andthe logarithm of the exchange rate and the FX volatility, σFX . However, itis important to realise that this equation defines a new share, Ft , quotedin the currency the option is quanto’d into rather than the share’s owncurrency. Ft is defined in such a way that a regular dollar option on Ftis in fact a quanto option on St 4dFt= (rlocal − ρσ S σFX ) dt + σ S dWt ,Ft
(19.2)
where
r ρ is the correlation between the logarithm of the stock price and thelogarithm of the exchange rate, where the exchange rate is quoted asnumber of dollars per pound. A positive correlation means that if thepound increases in value the stock price goes up.r rlocal is the risk free interest rate of the stock’s own currency. In BP’scase the rlocal is the risk free interest rate of the pound.From this equation it is obvious that anyone who holds a quanto calloption benefits if the correlation decreases and the holder of a quanto4The quanto model described in equation 19.2 is intuitive as the volatility, σ S , used to price the quanto optionshould be same as the implied volatility of the underlying stock, since the exchange rate is fixed and thereforethe option payout depends solely on the actual movement of the stock. The interest rate or drift part is slightlydifferent as the delta hedge is affected, see sub-section 19.2, by exchange rate movements and therefore affectsthe financing on the delta hedge. If for example the stock price doubles, this affects positively the financing on along call option (short shares at a higher stock level therefore receive more interest). However, if the correlationbetween the stock and the exchange rate is such that a doubling in stock price results in a halving of the dollarvalue against the pound, the hedge is unaffected and therefore has no impact on the financing of the delta hedge.Therefore it is obvious that the financing part of the quanto stock model is adjusted by −ρσ S σ F X .
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put benefits if the correlation increases. Depending on the sign of thecorrelation this formula also makes clear whether the holder of a quantooption is long or short FX volatility. If the correlation is negative theholder of a quanto call is long FX volatility and the holder of a quantoput is short FX volatility. If the correlation is positive the holder of aquanto call is short FX volatility and the holder of a quanto put is longFX volatility. Knowing that the model for the change in stock price fora USD stock with a dividend yield equal to d isdFt= (r$ − d) dt + σ S dWt ,Ft
(19.3)
shows that the price of a quanto option can be derived from a normal option by making an adjustment to the dividend yield of addingr$ − rlocal + ρσ S σFX to the dividend yield. In equation 19.3 r$ is theUSD risk free interest rate. This also shows that the main theme of aquanto option is the difference in forward compared to a regular option.
19.2 HEDGING FX EXPOSURE ONTHE QUANTO OPTIONHedging the FX exposure on the quanto option might not be very intuitivebut is very simple in practice. This is because the FX hedge is captured bythe delta hedge, which in turn is because the option notional in the localcurrency keeps changing with the changing FX. Namely, the notionalof the quanto option is agreed in the quanto currency and thereforethe notional in the local currency changes whenever the FX changes.This obviously implies that if the quanto currency halves in value withrespect to the local currency, the notional of the quanto option in thelocal currency halves and therefore the trader needs to halve his deltahedge even though the stock price might not have moved. The delta of thequanto option can easily be determined with the help of equation 19.2,the value of the stock in the local currency and the strike in the localcurrency.To show how the delta hedging of a quanto option works, which at thesame time captures the FX hedging of the quanto option, consider theexample in the introduction to this chapter. Suppose a trader sells thisATM quanto call option on BP with a strike of $ 5 and on a notional of10 million USD. Assuming that the parameters of equation 19.2 and astock value of 5 and strike price of 5 give this ATM option a delta of 0.5.As it was assumed that the exchange rate was 2 dollars per pound, the
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trader would need to buy 2.5 million pounds worth of BP stock as hisdelta hedge. Now suppose that USD halves with respect to GBP, whichmeans that the exchange rate goes to 4 dollars per pound. Just becauseof this change in exchange rate and without the stock price moving, thetrader would need to change his delta hedge to being long 1.25 millionpounds worth of BP stock. The trader therefore needs to sell 1.25 millionpounds worth of BP stock as a result of the exchange rate moving.The above shows that there is no need for a trader to put an FX hedgein place for a quanto option. However, the trader would need to swapout the FX on the premium received for the quanto option if he sold thequanto option. This is because equation 19.2 prescribes financing in thelocal currency. If the trader buys a quanto option he effectively ensuresfinancing in the local currency because he would first need to sell thelocal currency to buy the quanto currency in order to pay for the quantooption. Therefore the trader will only need to do an FX hedge if he sellsa quanto option, which is selling the quanto currency and buying thelocal currency on the premium amount. This ensures financing in thelocal currency.
20Composite Options1The composite option is designed for investors who want to executean option strategy on a foreign stock but want to fix the strike in theirown currency and get the payout of this option in their own currency.In contrast to the quanto option, where the holder gets a percentagereturn regardless of the exchange rate, the holder of a composite optionhas exposure to the exchange rate. One of the reasons that a compositeoption is traded is to protect the value in their own currency on a foreigninvestment. Consider the following example.
20.1 AN EXAMPLE OF THE COMPOSITE OPTIONA US investor owns stock in the British pharmaceutical Glaxo Smithkline (GSK). Assume that the current value of GSK is £ 13.00 and thatthe exchange rate is 2 dollars per pound. This means that the dollar valueof one share is $ 26. To protect this holding he buys a one year ATMcomposite put option on GSK. This means that the strike price of thiscomposite put option is equal to $ 26. Assume that after one year thestock goes down to £ 11.00 and the exchange rate goes from 2 dollars per pound to 1.5 dollars per pound (dollar increases in value). Thismeans that the dollar value of one GSK share has gone down from $ 26to $ 16.5. However, because the strike price of the composite option isfixed in dollars, the dollar loss on the shares is offset by the payout of thecomposite put option, which is equal to the strike price ($ 26) minus thenew dollar value of one GSK share ($ 16.5). In summary, the holder ofa composite option wants to protect the share value in his own currencyto both exchange rate movements and movements in the stock price.The best way to answer the question whether the holder of a composite option is short or long correlation is to model the change in stockprice, for a small time interval, in the currency of the composite. In theexample above this would be the dollar. Using the same notation as in1Parts of this chapter have been previously published in de Weert, F. (2006) An Introduction to OptionsTrading, John Wiley & Sons Ltd, Chichester. Reproduced with permission.
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Chapter 19, sub-section 19.1 the model looks as follows (see AppendixA):dFt= rcompo dt + σcompo dWt ,Ft
(20.1)
22σcompo= σ S2 + 2ρσ S σFX + σFX,
(20.2)
where
and rcompo is the risk free interest rate of the composite currency.This formula shows that the holder of a composite option is longcorrelation and the main theme is the difference in implied volatilitycompared to a regular option. Another way to visualise the USD composite put on GSK is by comparing it to a regular $ 26 put option on theGSK ADR.2
20.2 HEDGING FX EXPOSURE ON THECOMPOSITE OPTIONIf a trader sells the composite put option on GSK in the example ofsub-section 20.1, he obviously wants to delta hedge himself. Becauseequation 20.1 describes a composite option on stock as a normal optionon a stock in the composite currency, a delta can easily be determinedby setting strikes and share price in the composite currency. However,the trader can only execute his delta on the local stock, which is notquoted in the composite currency. This means that, even if the traderdelta hedges himself, he will still have an FX risk, as the payout on thecomposite option will be in the composite currency and his delta hedgeis in the local currency of the underlying stock. To illustrate this FX riskconsider the following.Suppose the trader hedges the short composite put option on GSK byjust delta hedging. This means by the example of sub-section 20.1 that,if the trader hedges the composite option on a δ = 1,3 he makes £ 2(13 − 11) per composite option, which is worth $ 3 at maturity as it wasassumed that the dollar increases from $ 2 per pound to $ 1.5 per pound.2ADR stands for Amercian Depository Receipt and is nothing more than a USD quoted stock on a companythat has its main listing in a different country.3Using δ = 1 is just for argument’s sake. Normally the delta would be much smaller at inception of an optiontrade and would converge towards one as the option becomes more in the money and gets closer to maturity.Whether the profit on the hedge is equal to the loss on the option ultimately depends on the volatility of both thestock and the FX, which is not taken into account in this example.
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As the dollar value of GSK goes from $ 26 to $ 16.5 during the termof the option, the trader loses $ 9.5 on the composite option and onlymakes $ 3 on his delta hedge. This obviously shows that just deltahedging is not enough. The trader would need to buy dollars on thenotional of his delta hedge to be fully immune to all the risks of thecomposite option on GSK. This means that, as an FX hedge, the traderwould sell £ 13 to receive $ 26 for every GSK share he shorted aspart of his delta at inception of the trade. At maturity the trader canbuy back these £ 13 for $ 19.5. The total profit on this FX hedge istherefore $ 6.5, making the profit on both the FX hedge as well as thedelta hedge equal to $ 9.5, which is equal to the loss on the compositeoption.To summarise the hedging of the FX exposure on a composite optionone just needs to realise that if one sells stocks as a delta hedge, one needsto also sell the currency the stock is quoted in and buy the compositecurrency in the same notional as the delta hedge. If the delta hedge is tobuy stock, the FX hedge is to also buy the currency the stock is quoted inand sell the composite currency in the same notional as the delta hedge.Obviously the FX hedge is not static and should be adjusted along withany delta adjustments. In other words, to be perfectly hedged againstboth stock movements and FX movements one needs to have, at anytime, the same notional of FX hedge as delta hedge.The above shows how to hedge the FX exposure of a composite option.However, it did not take into account that one also needs to put an FXhedge in place on the prem