# Tag Info

Accepted

### How to estimate real-world probabilities

The risk-neutral measure $\mathbb{Q}$ is a mathematical construct which stems from the law of one price, also known as the principle of no riskless arbitrage and which you may already have heard of in ...
• 13.8k

### Theoretical limits for contango and backwardation

This is a basic fact about futures trading and the storage of commodities. The phrase that was used by futures traders in the old days (and probably still today) was "the contango is limited by the ...
• 9,077
Accepted

### Derivation of VIX Formula

The piece you are missing is an approximation via the Taylor formula of the logarithm: $$\ln(1+x) \approx x-\frac{x^2}{2} \; .$$ Apply this to the first term in the final formula of the technical ...
• 1,487
Accepted

### Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

I provide a solution in three steps. The first step carefully outlines how to split up the expectation and what new measures are used. This first step does not require any special model assumption ...
• 13.8k

### How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

Let $P$ be the risk-neutral measure. We define the measure $P_S$ such that \begin{align*} \frac{dP_S}{dP}\big|_t &=\frac{S_t}{e^{rt}S_0}\\ &=e^{-\frac{1}{2}\sigma^2 t+\sigma W_t}. \end{align*} ...
• 20.4k

### Present and future role of pricing quants

FO is shrinking across the large investment banks. The market is not developing new products that will need new pricing formulas, if anything it is reverting to more vanilla structures. Nowdays FO ...
• 4,217
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• 6,743
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### Black-Scholes formula for Poisson jumps

We assume that the process $\{J_t, \, t\ge 0\}$ is defined at the jump times of the Poisson process $\{N_t, \, t \ge 0\}$, and all the jump sizes are independent and identically distributed. That is, \...
• 20.4k

### Why discounted derivative price is a martingale?

Under a Black-Scholes framework, the dynamics of the stock price under the risk-neutral measure $\mathbb{Q}$ are given by ... $$S_t = r S_tdt +\sigma S_tdW^{\mathbb{Q}}_t$$ ... and those of the ...
• 7,101
Accepted

### The dice game and derivatives trading

The interviewer meant that he's smart. Quoting Senior VP of People operations at Google, On the hiring side, we found that brainteasers are a complete waste of time. How many golf balls can you ...
• 6,334

### CMS Pricing - Convexity Adjustment by Replication

The CMS represents the value of a swap rate for any point in time, i.e. we are interested in extrapolating the density of the swap rate in a similar way as the IBOR rate. Let us start with the fair ...
• 1,002
Accepted

### Static vs Dynamic Hedging: when is each one used?

It depends a little bit what you're trying to do. If you can statically replicate the payoff of a position at $t=0$, then putting on that hedge will insulate you from all risk coming from the ...
• 2,846

### How do market makers calculate the IV for options?

They do not calculate it, they set it at a market clearing level based on supply and demand. It is similar to the way equity market makers set the price of a stock: a lot of buyers => raise the ...
• 9,462
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• 4,891
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### Curve Euribor - Euribor 3M

It is incorrect to use 1m euribor or O/N euribor in a 6m Euribor forward curve. You should only use instruments based on 6M euribor, such as 1x7 FRA, 6x12 FRA or swaps v 6m Euribor, as you have done ...
• 304

### What is a Constant Maturity Swap (CMS) rate?

In simple terms: An ordinary swap might be a 10 year swap of Libor vs a fixed rate; this fixed rate is determined in the marketplace every day and is published by Reuters, Bloomberg etc. as the '10 ...
• 9,077
Accepted

### Derive vega for Black-Scholes call from this formula?

Note that, \begin{align*} \frac{\partial{C}}{\partial{\sigma}} &=\frac{S_0}{\sqrt{2\pi}}{e^\frac{-d_+^2}{2}}(\frac{-1}{\sigma})(d_-)-\frac{Ke^{-rt}}{\sqrt{2\pi}}e^{\frac{-d_-^2}{2}}(\frac{-1}{\...
• 20.4k

### Using a Constant as a Numeraire

A Numeraire must be a tradeable asset. If you can find a constant tradeable asset, then yes a constant can be used as a numeraire.
• 1,329