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PDE and Black Scholes problem

Consider Black Scholes problem $\frac{\partial V}{\partial t} + \frac{\sigma^2 S^2}{2}\frac{\partial^2V}{\partial S^2} + rS\frac{\partial V}{\partial S} -rV = 0$ with boundary condition $V(S,T)=f(S)$, ...
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164 views

Solving Black-Scholes PDE using Laplace transform

I'm trying to obtain the Laplace transform of Call option price with repect to time to maturity under the CEV process. The well known Black scholes PDE is given by $$ ...
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2answers
197 views

Black-Scholes Equation - Riskless portfolio derivation

The following is a summary of the derivation of the Black-Scholes equation as given on wikipedia (http://en.wikipedia.org/wiki/Black-Scholes_equation#Derivation) - I have a question regarding the ...
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1answer
151 views

Heat/Diffusion Equation

I am working on a problem where I have successfully reduced a version of Black Scholes to the Heat Equation and then shown the solution to be: ...
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1answer
153 views

Does Implied Volatility always exist?

I am considering a simple Heston Model Market with one risky and one riskless asset. The dynamics of the riskless asset is simply $dB_t=r*B_t*dt$ The dynamics of the risky asset is as follows, $ ...
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American Swaption Pricing with PDE discretization

So I am still trying to price an american swaption. (MC approach here: American Swaption Pricing with Monte-Carlo method) I've found in Paul Wilmott, The mathematics of financial derivatives, a PDE ...
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1answer
229 views

American Swaption Pricing with Monte-Carlo method

I want to price an American swaption but I am not sure about what I am doing. Tree methods and PDE discretization seem difficult to adapt to a swaption. I am trying a Monte-Carlo approach. (in ...
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0answers
73 views

Approximating the PDE price of an option with a binomial model

I'm trying to replicate, with a binomial model, the price of an option obtained with a PDE. It doesn't really work, so I was wondering, if there are some caveats when doing that. The PDE model use a ...
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342 views

Black--Scholes hedging argument

I'm trying to understand the standard hedging argument to derive the Black--Scholes PDE. There's one aspect of the derivation which I can't get passed and I'd be very grateful for some clarification ...
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3answers
158 views

The reason behind the selection of a 1 standard deviation movement for self financing delta hedge

I'm learning this material and I can follow the derivation of the BSM PDE fairly well. The only problem I have is there is an assumption in the derivation (that I am reading) that a stock price ...