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# Questions tagged [black-scholes-pde]

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### American option PDE [closed]

I'm reading the pdf here regarding the PDE associated with the American option. Essentially, one would turn the Black Scholes PDE into an inequality. Suppose you're pricing an American put where $S$ ...
• 101
0 votes
2 answers
207 views

### Quantifying Costs/Benefits Of Partial Hedging

Say I sold a long-dated European put option and I want to analyze the costs and benefits of partial hedges in a world with stochastic price movements, rate movements, and volatility. For example, let'...
0 votes
1 answer
95 views

### Is the Black Scholes PDE actually immediate from Ito's lemma?

Ito's lemma replaces $dS^2$ by $vol^2*dt$, however it is repeatedly mentioned that the lemma manifests in the integral form and the differential form below is merely a short hand for the integral form:...
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0 answers
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### Continuous flows Perpetual maturity cap on Exchange Options PDE Change of variable

Im trying to do a change of variable on the following PDE Using the following change of variable $$V(P^1,P^2) = P^2 W(C), C=\frac{P^1}{P^2}$$ I get this for the homogeneous part of the equation: ...
2 votes
1 answer
289 views

2 votes
1 answer
318 views

### How to find IV from market prices accodring to Bergomi

I was conviced to read Bergomis book on stochasic volatility to learn how options are traded in practice. He basically writes that the probabilisitc side is rather useless and that one only uses the ...
4 votes
1 answer
233 views

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2 votes
2 answers
2k views

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1 vote
1 answer
113 views

### Sensitivity Approximation - Crank Nicolson

I am looking into a new method of calculating sensitivities starting off with a proof of concept with Black Scholes PDE. Suppose I want to calculate Rho and take the derivative of the PDE (heresy!!) ...
• 11
1 vote
1 answer
457 views

### Modifying Basic Black Scholes Equation For Time Dependent Variables - Per Wilmott?

I am reading Wilmott's book and don't understand why he makes the following step to re-write the PDE. I get equation 8.4, that's just the typical PDE for a dividend yielding stock where r(t), D(t) ...
• 267
2 votes
0 answers
130 views

### What is the recipe for deriving a PDE for the price of an option?

In the Black Scholes setting, here is how my understanding is of how we derive the PDE for the value of an option. We assume that the price of the option is Markovian in our state variable $S_t$. ...
• 21
2 votes
1 answer
175 views

### Is it possible to transform arithmetic-average strike continuous sampling Asian Black-Scholes equation to a heat equation?

By Transformation from the Black-Scholes differential equation to the diffusion equation - and back, we are able to transform vanilla European option into a heat equation. And we know that the ...
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2 votes
1 answer
103 views

### Numerical Solution to 3 Dimensional Backward BS PDE

I have a three dimensional backward BS PDE.  \frac{\partial V}{\partial t} + a(t) S \frac{\partial V}{\partial S} + \frac{1}{2} \sigma(t, S)^2 \frac{\partial^2 V}{\partial S^2} + b(t, M) \frac{\...
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