金融论文范文|高级金融数学作业代写 Advanced Financial Mathematics Notes

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

高级金融数学作业代写

Denote by Et,x the expectation conditioned on the event X(t)=x

高级金融数学作业代写

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

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高级金融数学作业代写

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,

高级金融数学作业代写

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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