Math 5965 Discrete Time Financial Modelling T1 2023 Tutorial Week 4
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Tutorial Week 4
Math 5965 Discrete Time Financial Modelling
T1 2023
1. Consider a non-dividend paying stock whose initial stock price is 62 and which has a log-volatility of σ = 0.20. The interest rate T = 10%, compounded monthly. Consider a 5-month option with a strike price of 60 in which after exactly 3 months the purchaser may declare this option to be a (European) call or put option.
Assume u = 1.05943 and d = 
= 0.94390
(a) Compute the values of the binomial lattice for 5 1 month period.
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5 |
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62 |
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Compute the appropriate risk-free rate.
Find the risk-neutral probability p˜ of going up?
Find the values of call option and put option along this lattice:
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5.85 |
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call |
option |
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0 |
1 |
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3 |
4 |
5 |
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1.40 |
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put |
option |
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2. (Shreve, Exercise 2.2) Consider the following modelling
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S0 = 4 |
S1 (H) = 8 S1 (T) = 2 |
S2 (HH) = 16 S2 (HT) = S2 (TH) = 4
S2 (TT) = 1 |
S3 (HHH) = 32
S2 (HHT) = S3 (HTH) = S3 (THH) = 8 S3 (HTT) = S3 (THT) S3 (TTH) = 2 S3 (TTT) = 0.5 |
(a) What is the distribution of S3 under the risk-neutral probability p˜ = 
, q˜ = 
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(b) Compute 
S1 , 
S2 , 
S3 . What is the average rate of growth of the stock price under 
?
(c) Answer (a) and (b) again under the actual probabilities p = 
and q = 
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2023-04-22