Pricing American Options - an Important Fundamental Research in ...

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An Exact Solution in Series Expansion Form In the above PDE system, – X is the strike price of the option; – r is the risk-free interest rate; – σ is the volatility of the underlying asset price. In the current solution, r and σ are assumed to be constant. IWIF-II www.swingtum.com/institute/IWIF PPT 32/68 Song-Ping Zhu, SMAS, April 26, 2007 0-31
An Exact Solution in Series Expansion Form The normalized PDE system becomes ⎧ ⎪⎨ ⎪⎩ − ∂V ∂τ + S2 ∂2 V ∂V + γS − γV = 0, ∂S2 ∂S V (S f (τ), τ) = 1 − S f (τ), ∂V ∂S (S f (τ), τ) = −1, lim V (S, τ) = 0, S→∞ V (S, 0) = max{1 − S, 0}, in which γ ≡ 2r can be viewed as an interest rate relative to the σ2 volatility of the asset price. IWIF-II www.swingtum.com/institute/IWIF PPT 33/68 Song-Ping Zhu, SMAS, April 26, 2007 0-32
Page 1 and 2: Faculty of Informatics, University
Page 3 and 4: Background What is an option? What
Page 5 and 6: Review of Various solution Approach
Page 7 and 8: A Figure in Zhu and Zhang (2007b) 1
Page 17 and 18: A. Basso, M. Nardon and P. Pianca
Page 19 and 20: 1 γ=5 0.9 0.8 0.7 B(τ) 0.6 0.5 0.
Page 27 and 28: An Exact Solution in Series Expansi
Page 31: An Exact Solution in Series Expansi
Page 51 and 52: The Solution for the Option Price
Page 55 and 56: Examples and Discussion Verificatio
Page 57 and 58: Examples and Discussion 100 95 90 A
Page 59 and 60: Examples and Discussion 100 90 80 7
Page 61 and 62: Examples and Discussion 40 38 The n
Page 63 and 64: Examples and Discussion 40 35 30 Op
Page 65 and 66: Examples and Discussion Example 3:
Page 67 and 68: Examples and Discussion 100 90 80 7

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