Advanced Financial Mathematics Notes
高级金融作业代写 the derivative of the option price with respect to the underlying, called the delta of the option, has to be equal to the number
Feynman-Kac Theorem 高级金融作业代写
Theorem: let X be a diffusion satisfying
Denote by
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
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
• 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
Proof 高级金融作业代写
delta of an option
is called 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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