Questions tagged [malliavin-calculus]
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9
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Is the time derivative of asset returns expressible as an SDE?
Consider the following SDE for $(S_t)_{t\geq 0}$ under $\mathbb{Q}$,
\begin{equation}
\mathop{dS_t}=S_t\left(r\mathop{dt}+\sigma(t,S_t)\mathop{dW_t}\right),
\end{equation}
which (in Langevin form) may ...
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Derivation of Bergomi model
In Stochastic Volatility Modeling, L. Bergomi introduces in Chapter 7 the pricing equation (7.4) :
$$
\frac{dP}{dt}+(r-q)S\frac{dP}{dS}+\frac{\xi^t}{2}S^2\frac{d^2P}{dS^2}+\frac{1}{2}\int_t^Tdu\int_t^...
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Malliavin calculus on two different probability spaces
I'm studying Malliavin Calculus recently. I have two different text books, one is the lecture note written by Oksendal, and the other is a book (Introduction to Malliavin Calculus) by Nualart.
In this ...
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Anticipating stochastic integral $\int_0^T W_T dW_t$
Using basic techniques from Malliavin calculus it can be shown that
$$
\int_0^T W_T dW_t = W_T^2 - T
$$
As can be seen the above integral is a non-adapted stochastic integral.
We also know using Ito ...
user34971
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Martingale representation of European option
Let stock price $S$ satisfy
$$S(t)=S(0)e^{(\int_0^t\sigma(s)dB_s-\frac{1}{2}\int_0^t\sigma(s)^2ds)}$$
I want to calculate the Martingale representation $V(t)=E(F|F_t)$ of European option with strike ...
- 161
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Computing Malliavin Derivative for European Call Payoff
Let $X_t$ be a continuous local-martingale modeling the stock price given by
$$
X_t = \int_0^t \sigma_t(T,K)dW_t
,
$$
and $\sigma_t(T,K)$ is an $L^2$-measurable process not adapted to $W_t$'s ...
- 353
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Using malliavin derivative to find the worst Delta-positive hedge?
Background:
I've heard that Malliavin Calculus can be used to show the explicit form of a delta-neutral hedge (given an SDE driven market model). For example, here is a sketch here on page 21 on how ...
- 353
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American Swaption Heding with Malliavin Calculus
Hedging American Swaption
Hello, I priced an American swaption using Black model with swap rates diffusion to find the european (call) price at t.
$$ C_t = (\delta \sum_{j=n+1}^{M+1} Z_t^{T_j})[R(t,...
- 1,217
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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.
...
- 1,217