# Tag Info

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 ...
• 16.2k
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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 ...
• 1,527

### Which models do Bloomberg/Reuters use to derive implied volatility for interest rate derivatives with negative forward rates?

Short Version Market standard (since the low interest rate environment after 2008) is to use Normal Vol (used in the Normal / Bachelier model) Market data comes from contributors like Tullett, ICAP ...
• 9,394
Accepted

### 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 ...
• 9,402
Accepted

### 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 ...
• 11.8k
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• 6,993
Accepted

### 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, \...
• 21.2k

### 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 ...
• 8,169
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 ...
• 7,004

### 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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• 8,169
Accepted

### Replicating a square derivative with calls and puts

Note that \begin{align*} S_T^2 = 2\int_0^{S_T} k dk. \end{align*} Then \begin{align*} S_T^2 &= 2S_T^2-2\int_0^{S_T} k dk\\ &=2S_T\int_0^{S_T}dk-2\int_0^{S_T} k dk\\ &=2\int_0^{S_T} (S_T-k)...
• 21.2k

### Cash-settled swaptions

The advantage of cash-settled swaptions is that the payoff only depends on one variable: the corresponding swap rate which is directly observable in the market:  \mathrm{Payoff}(T) = f(S_T) = A^{\...
• 3,946

### Refer some most recent books of derivatives pricing by C++

If by "modern C++" you mean C++11 and beyond, I'm afraid you won't find such a book at this time. If you are content with idiomatic C++ 03, as in "using the STL and smart pointers instead of managing ...
• 7,853