Advanced Financial
Mathematics Notes
高级金融数学作业代写 Consider an option with a payoff g(S(T )).The price at time t of this option is given by C(t, S(t)), where function C is a
Feynman-Kac Theorem 高级金融数学作业代写
Theorem: let X be a diffusion satisfying
Denote by Et,x the expectation conditioned on the event X(t)=x
for some given functions r, g, and f . Under technical conditions, function V is the solution to the Feynman-Kac PDF and the boundary conditions 高级金融数学作业代写
The price of a contingent claim with a random pay-off C at maturity T is computed based on Expectation Formula
The zero-coupon T -bond that pays 1 dollar at time T has the price
Application of Feynman-Kac 高级金融数学作业代写
- C: a contingent claim
- Then,
Black Scholes Equation
• Consider an option with a payoff g(S(T )).The price at time t of this option is given by C(t, S(t)), where function C is a solution to the
Black-Scholes PDE and the boundary condition 高级金融数学作业代写
Proof
delta of an option
the derivative of the option price with respect to the underlying, called the delta of the option, has to be equal to the number of shares of
stock held by the replicating portfolio.
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