Lecture7_BinomialOptionPricing

Exercise see the x axis denotes the stock price whats

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Unformatted text preview: changes - See the bottom of “Option” tab. See - The x-axis denotes the stock price (S) - What’s the finding? 15-31 How American option prices react to input changes: volatility changes - Exercise 2: See the bottom of “Option” tab. Exercise See - The x-axis denotes the stock price (σ) - What’s the finding? 15-32 VBA for American option pricing See the function “binomial_all” in “VBA_Amer” See tab tab It gives the price 2.37, consistent with our trees Let’s use a “smaller” tree (2 steps) for illustration Call or Put (c or p) Stock price (S) Strike price (K) Maturity ( T ) riskfree Rate ( r ) Dividend payout Rate ( q ) Volatilty (sigma) Number of steps (n) p 100 100 1 5.0% 0.0% 20.0% 2 Step (dt) u d p emrdt 0.5000 1.1519 0.8681 0.5539 0.9753 15-33 Stock price in the tree 100 115.19 86.81 Put option price in the tree 5.74 132.69 100 75.36 0 0 13.19 0 24.64 15-34 Details in the code *** (1) In the program “binomial_all”, we step back the tree For j = n - 1 To 0 Step -1 For I = 0 To j For If Style = "euro" Then If price(I) = pv * (Pu * price(I) + Pd * price(I + 1)) price(I) ElseIf Style = "amer" Then ElseIf price(I) = pv * (Pu * price(I) + Pd * price(I + 1)) price(I) S(I) = S(I) / u S(I) price(I)=Application.WorksheetFunction.Max(price(I),C_P*(S(I)-strike)) price(I)=Application.WorksheetFunction.Max(price(I),C_P*(S(I)-strike)) End If End Next I Next Next j 15-35 Details in the code *** (1) If Style = "euro" then what we have is the same as If “binomial_euro” “binomial_euro” If Style = “amer" then we adjust for American options: price(I) = pv * (Pu * price(I) + Pd * price(I + 1)) – the same S(I) = S(I) / u – we let stock price go to the prior step S(I) price(I)= Max(price(I),C_P*(S(I) - strike)) – replace the option price by the bigger value from option (a) the present value of waiting for the next step (a) (b) the current payoff from exercising the option (b) See the next slide for an example See 15-36 Details in the code *** (2) 5.74 0 0 13.19 0 24.64 (a) the present value of waiting for the next step = 0.9753* ( 0.5539*0 + (1-0.5539)*24.64) = 10.72 0.9753* (b) the current payoff from exercising the option (b) = Max(-1*(100 – 86.81), 0) = 13.19 Max(-1*(100 As a result, the price of the American option = 13.19 in this As node node 15-37 The approximation of American put option prices In the tab “approximation" we try to see how American put In option prices as steps (x-axis) go up option 15-38 The approximation of American call option prices In the tab “approx2“, we try to plot the chart for call option In price given all other input are the same price 15-39 Appendix: Not for exam 15-40 Equation of tree...
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This document was uploaded on 03/03/2014.

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