Question

Compute the fair value of a chooser option which expires after n = 10n=10 periods. At expiration the owner of the chooser gets to choose (at no cost) a European call option or a European put option. The call and put each have strike K = 100K=100 and they mature 5 periods later, i.e. at n = 15n=15

Instructions: Quiz Instructions: Option Pricing in the Multi-Period Binomial Questions 1-8 should be answered by building a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with: T = .25T=.25 years, S_{0} = 100S 0 ​ =100, r = 2\%r=2%, \sigma = 30\%σ=30% and a dividend yield of c = 1\%.c=1%. Hint Your binomial model should use a value of u = 1.0395...u=1.0395.... (This has been rounded to four decimal places but you should not do any rounding in your spreadsheet calculations.) Submission Guidelines Round all your answers to 2 decimal places. So if you compute a price of 12.9876 you should submit an answer of 12.99.

Answer 1

Solution: p_chooser = 10.81245

chooser.p <- OptionPrice(100, mtrty = 0.25, prd = 15, r = 0.02, dvd = 0.01, sigma = 0.3, strike = 100, call = FALSE)
chooser.c <- OptionPrice(100, mtrty = 0.25, prd = 15, r = 0.02, dvd = 0.01, sigma = 0.3, strike = 100)
chooser <- pmax(chooser.c$Payoff, chooser.p$Payoff)[1:11, 1:11]
r.real <-  exp(0.02*0.25/10)
discount(chooser[1:11,1:11], q = 0.49247, maturity = 0.25, r = r.real)

Output

> discount(chooser[1:11,1:11], q = 0.49247, maturity = 0.25, r = 0.02)
          [,1]     [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]      [,9]     [,10]     [,11]
 [1,] 10.81245 11.08461 12.324800 14.585646 17.809620 21.819826 26.368571 31.250030 36.394629 41.761927 47.343416
 [2,]  0.00000 10.55546  9.888508 10.139137 11.466918 13.930107 17.420391 21.649281 26.278614 31.210502 36.373491
 [3,]  0.00000  0.00000 11.209553  9.651811  8.857415  9.084352 10.552541 13.328428 17.171535 21.510333 26.221217
 [4,]  0.00000  0.00000  0.000000 12.728436 10.428976  8.643030  7.665696  7.865955  9.608114 12.972762 16.953365
 [5,]  0.00000  0.00000  0.000000  0.000000 14.968025 12.168778  9.597041  7.476415  6.180659  6.349616  9.118798
 [6,]  0.00000  0.00000  0.000000  0.000000  0.000000 17.694042 14.672197 11.661045  8.738632  6.020775  3.666776
 [7,]  0.00000  0.00000  0.000000  0.000000  0.000000  0.000000 20.637842 17.603637 14.504401 11.381583  8.308878
 [8,]  0.00000  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000 23.595568 20.622473 17.544082 14.370588
 [9,]  0.00000  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 26.495943 23.623065 20.634933
[10,]  0.00000  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 29.300977 26.538048
[11,]  0.00000  0.00000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000 32.001170