# Questions tagged [malliavin-calculus]

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### Anticipating stochastic integral $\int_0^T W_T dW_t$

Using basic techniques from Malliavin calculus it can be shown that $$\int_0^T W_T dW_t = W_T^2 - T$$ As can be seen the above integral is a non-adapted stochastic integral. We also know using Ito ...
0answers
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### Martingale representation of European option

Let stock price $S$ satisfy $$S(t)=S(0)e^{(\int_0^t\sigma(s)dB_s-\frac{1}{2}\int_0^t\sigma(s)^2ds)}$$ I want to calculate the Martingale representation $V(t)=E(F|F_t)$ of European option with strike ...
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### Computing Malliavin Derivative for European Call Payoff

Let $X_t$ be a continuous local-martingale modeling the stock price given by $$X_t = \int_0^t \sigma_t(T,K)dW_t ,$$ and $\sigma_t(T,K)$ is an $L^2$-measurable process not adapted to $W_t$'s ...
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### Using malliavin derivative to find the worst Delta-positive hedge?

Background: I've heard that Malliavin Calculus can be used to show the explicit form of a delta-neutral hedge (given an SDE driven market model). For example, here is a sketch here on page 21 on how ...
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278 views

### American Swaption Heding with Malliavin Calculus

Hedging American Swaption Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t.  C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
2answers
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### Malliavin Calculus

From a quant point of view, how would you explain Malliavin calculus in few words ? I have the level to take these courses, but won't be able to do it next year, so I want to know what I am missing. ...