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1answer
395 views

How to get Geometric Brownian Motion's closed-form solution in Black-Scholes model?

The Black Scholes model assumes the following dynamics for the underlying, well known as the Geometric Brownian Motion: $$dS_t=S_t(\mu dt+\sigma dW_t)$$ Then the solution is given: ...
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2answers
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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 ...
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2answers
336 views

SVCJ (SVJJ) Duffie et. al Model implementation in Matlab

I'm attempting to implement aforementioned SVCJ model by Duffie et al in MATLAB. so far without success. It's supposed to price vanilla (european) calls . parameters provided, the expected price is: ...
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2answers
1k views

Why Ito calculus?

Coming from physics, I am used to the fact that the Ito interpretation of most natural stochastic equations is wrong, and one should be using Stratonovich calculus instead (of course they are ...
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6answers
874 views

Self-financing and Black-Scholes-Merton formula

Self-financing is an important concept in financial product replicating, normally used in pricing. I read about several ways to derive Black-Scholes-Merton (BSM) formula. Seems some approaches ...
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1answer
170 views

Girsanov theorem in CMS convexity derivation

I am going through the derivation of CMS convexity from the notes of Lesniewski There is a transformation from $T_p$ forward measure to annuity measure $Q$ as $$ ...