Consider a 11-period binomial model with R=1.02R=1.02, S_0 = 100S 0 =100, u=1/d= 1.05u=1/d=1.05. Compute the value of a European call option on the stock with strike K=102K=102. The stock does not pay dividends. Please submit your answer rounded to two decimal places. So for example, if your answer is 3.45673.4567 then you should submit an answer of 3.463.46. 1 point
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Ответ:
1.76
Explanation:
Given the following :
R=1.02,
S0 = 100
u=1/d= 1.05
Strike(k) = 102
Total Payoff = (probability of upside × upside Payoff) + (probability of downside × downside Payoff)
Upside Price = u × S0 = 1.05 × 100 = 105
downside Price = S0/u = 100/1.05 = 95.24
Upside Payoff = upside price - strike rate =(105 - 102) = 3
Upside probability :
[e^(r - q) - d] / u - d
E = exponential, q = Dividend (Dividend is 0, since the stock does not pay dividend)
d = 1/d = 1/1.05 = 0.9523809
e = 2.7182818
[2.7182818^(1.02% - 0) - 0.9523809] / (1.05 - 0.9523809)
[1.0102521 - 0.9523809] / 0.0976191
0.0578712 / 0.0976191
= 0.5928266
Probability of downside = 1 - p(upside)
P(downside) = 1 - 0.5928266
P(downside) = 0.4071733
Therefore, total Payoff =
(0.5928266 × 3) + (0.4071733 × 0)
= 1.7784798
European. Call option:
Total Payoff / (1 + r%)
1.7784798 / (1 + 1.02%)
=1.7784798/ (1 + 0.0102)
= 1.7784798 / 1.0102
= 1.7605224
= 1.76
Ответ: