# Tag Info

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### 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 ...
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### 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 ...

### 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 ...
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### 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 ...

### 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*} ...

### 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 ...

### Innovative ways of visualizing financial data

Although quite simple connected scatterplots can give interesting new insights on how time series perform together: http://steveharoz.com/research/connected_scatterplot/ As an example: Gold vs. S&...
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### When would open interest equal trading volume?

Futures are in "zero net supply", or "for every long there is a short", which means that at any time there are investors who are long a certain number of contracts and other investors who are short an ...
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### Impact on DV01 of cbot bond futures by changing coupon from 6% to 4%

It's complicated. Assuming there is no CTD switches, then yes, the theoretical modified duration should be unchanged and the DV01 will be lower. For simplicity, imagine that there is only one bond ...
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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, \...

### 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 ...
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### 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 ...

### 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 ...
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### 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 ...

### 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 ...
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### What is the Radon-Nikodym derivative in the Heston model?

Let \begin{align*} \mathrm{d}S_t&=\mu S_t\mathrm{d}t+\sqrt{v_t}S_t\mathrm{d}B_{S,t}, \\ \mathrm{d}v_t&=\kappa(\bar{v}-v_t)\mathrm{d}t+\xi\sqrt{v_t}\mathrm{d}B_{v,t}, \end{align*} where \$\...
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### Differences between main classes of interest pricing derivatives models

I am not sure if you can classify it like that. Mind you, I never wrote a book. I'll write what I know below and you can decide if the classification makes sense or not. 1 ) STIR: as the term ...

### What is meant by the funding cost of a derivative?

The theory for pricing derivatives is based on self-financing trading strategies that replicate all the payoffs of the derivative. Hence, derivatives pricing requires funding at the risk free rate, ...
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### Calculating DV01 for Treasury Futures with CTD switch risk

You are trying to calculate the so-called "option-adjusted DV01" (OA DV01). The nice thing about OA DV01 is that it's a smooth function of yield shifts. I'm going to be lazy here and simply ...
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### the cash flows behind closing out futures positions

Futures contracts are marked to market every day. This mean that each evening cash is added to or subtracted from your account as a result of the price movement that day. When you close out your ...