Applications of Least-Squares Regressions to Pricing and by Andreas J. Grau PDF

By Andreas J. Grau

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We denote the stock price at time t with St and the option price in dependence of St := {Sτ |τ ∈ I}, I ⊆ [t0 , t] with Vt := V (St , t). 19)), 1 ∂ 2 Vt ∂Vt ∂Vt + σ 2 St2 − rVt = 0 + rSt 2 ∂t 2 ∂St ∂St with risk-free interest rate r. Now, the peculiarity of the MWAO is expressed by a boundary condition to the option value V , known as an American constraint. 3 Moving Window Asian Option 55 where P is the option’s payoff function that depends on the current stock price St and a weighted average At of the historic stock prices using the weight function α.

For a discretely sampled Asian call option with sample dates t0 = 0, t1 , . . , tT , the payoff P is P (S) = max(I(S) − K, 0), for an Asian call option resp. P (S) = max(K − I(S), 0) for an Asian put option with I(S) = 1 T +1 T Sti . 2) where θi,j , i = 1 . . T , j = 1 . . n, denotes independent realizations of a random variable drawn from a standard normal distribution. The value Vt0 is the no-arbitrage price of the standard Black-Scholes option price model. 1)), the Asian option pricing problem can be divided into an expected payoff function and the probability density function pStT of the asset price at maturity.

Under Reference MC, the prices were computed using the regular Monte Carlo technique. 1) with estimates for the pdf pStT (s) ≈ p˜StT (s) resp. the conditional expectation f (s) ≈ f˜(s). 000 option valuations and thus an expected error for a single valuation. 001 Summary of the Feature Extraction for European Path Dependent Options For discretely observed European style path dependent options, the new method can be summarized as follows: 1. Compute the local basis approximation of the expected payoffs f (StT ) = EQ [P (S)|StT = s] for all possible asset path histories S := {Sτ |τ ∈ I}, I ⊆ {t0 , t1 , .

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Applications of Least-Squares Regressions to Pricing and Hedging of Financial Derivatives by Andreas J. Grau

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