Quantitative Finance Weekly Newsletter

Quantitative Finance newsletter

Top new questions this week:

What's the point of discounting in risk-neutral pricing?

Let $\phi$ be a self-financing strategy that replicates a time $T$ option payoff $X$ on stock $S$. By definition of a trading strategy, $\phi$ is previsible. Finally, let $V_t$ be the time $t$ value ...

options option-pricing  
asked by bcf 6 votes
answered by user9403 3 votes

Speeding up computations: when to use Quasi and standard Monte-Carlo in pricing

I am familiar with the theory of Monte-Carlo techniques in the numerical integration, and recently I have started my experiments with these methods applied to derivatives pricing. I am using ...

option-pricing monte-carlo numerical-methods low-discrepancy-sequences  
asked by Ulysses 4 votes

Multidimensional Ito's Lemma for Vector-Valued functions

Consider the vector of $n$ Ito processes $$ d \mathbf{X}_t = \mathbf{\mu}(\mathbf{X}_t,t)dt + \Sigma(\mathbf{X}_t,t)d\mathbf{W}_t $$ where $\mathbf{\mu} \in \mathbb{R}^n$ and $\Sigma \in ...

stochastic-calculus itos-lemma  
asked by bcf 4 votes
answered by quasi 4 votes

Why Lie groups, differential geometry and string theory relate to MF?

I'm reading Peter Carr's "A Practitioner’s Guide to Mathematical Finance". When talking about the math used in mathematical finance, he mentions Lie groups, differential geometry, string theory. Can ...

reference-request quants  
asked by SiXUlm 4 votes
answered by vanna 3 votes

Variance replication using options

I would like to understand the intuition behind the following question: Why a certain weighted sum of prices of put and calls is equivalent to the implied variance of an underlying? A variance swap ...

options volatility implied-volatility variance  
asked by Escachator 3 votes
answered by Gordon 6 votes

Need for Binomial Representation Theorem

In some texts (e.g. Baxter & Rennie, Shreve I) the binomial model is first constructed using the usual backward induction argument, and it is concluded that by no-arbitrage the time $t$ value of a ...

asked by bcf 3 votes
answered by bcf 0 votes

How to check that an interest rate curve is arbitrage free

I have 2 interest rate curves (LIBOR 3M and OIS). I want to create stress scenarios for those two curves. Is it possible that some scenarios will make my term structure arbitrageable? How can I test ...

interest-rates arbitrage no-arbitrage-theory term-structure stress-testing  
asked by mickG 3 votes

Greatest hits from previous weeks:

Exercising an American call option early

I have seen the rationale behind why it is never optimal to exercise an American call option early, but have a question about it. If the option strike price is $E=\$20$ and it expires at $T=1yr$, if ...

asked by dplanet 4 votes
answered by chrisaycock 7 votes

Worked examples of applying Ito's lemma

In most textbooks Ito's lemma is derived (on different levels of technicality depending on the intended audience) and then only the classic examples of Geometric Brownian motion and the Black-Scholes ...

stochastic-calculus reference-request itos-lemma  
asked by vonjd 8 votes
answered by emcor 10 votes

Can you answer these?

Bloomberg scripting language (BLAN)

Did anyone work with Bloomberg scripting language (BLAN is the name I guess). If so is it really flexible and is it competitive with other valuation services (say Super Derivatives). Does it enable ...

programming derivatives bloomberg exotics  
asked by jakub 2 votes

pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...

stochastic-processes stochastic-calculus probability markov poisson  
asked by stochastic_newbie 2 votes

Using FX ATM Volatility to Estimate Smile

Suppose $S$ is some FX rate, EUR/USD say, and $\sigma_{S}(K,T)$ is the implied volatility for some option written on $S$, sourced from the surface $\sigma_{S}(\cdot,\cdot)$ (alternatively, consider ...

options option-pricing implied-volatility fx valuation  
asked by Taylor Martin 2 votes
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