Binomial - Risk neutral probability and value of call option

17. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the risk-neutral probability of a 10% rise in both quarters?
a. 0.10
b. 0.24
c. 0.36
d. 0.60
e. 0.84

18. A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the value of the call option?
a. $6.25
b. $5.55
c. $5.00
d. $4.50
e. $4.05

Solution Preview

See the attached file. The correct answers are c 0.36 and b 5.55

A stock price is currently $100. Over each of the next two three-month periods it is expected to increase by 10% or fall by 10%. Consider a six-month European call option with a strike price of $105. The risk-free rate is 8%. What is the risk-neutral probability of a 10% rise in the first ...

Solution Summary

Illustrates the use of binomial tree model for calculation of Risk neutral probability and value of call option with two conceptual questions. Solution provide detailed answers.

... up state (1 - Pr) = Risk-neutral probability of a ... formulas using binomial risk-neutral option pricing ... can calculate the risk-neutral probabilities from formula ...

... assumptions (geometric Brownian motion theory of price behaviour, risk-neutral valuation, etc ...Binomial model. ... cise built into the model tant risk free rate can ...

... (a) Compute the risk-neutral probabilities for the ... The solution discusses pricing options on a binomial tree. Answer: ... Now,. (a) Risk neutral probability for the ...

... you are using the 2-stage binomial option pricing formula. You take the risk neutral probabilities (in this case 0.5 ... it is (probability*payout)/(1+risk free rate ...

... combination of call options, the other on Binomial tree ... You don't know the probabilities of the two ... For risk neutral valuation 130β-20 = 80β orβ= 0.40 =20 ...

... free world; therefore XN(d2) is the probability that the ... and zero otherwise in a risk neutral world ... lso Binomial model can be used for valuing both American and ...

... For risk neutral valuation, both the outcomes should give ... Riskless portfolio must earn the risk free rate ... European put options We construct binomial trees to ...

... reduces to two main themes, (1) arbitrage-neutral pricing and (2) the binomial interest rate tree ... opportunity allows for a greater than risk-free return ...

... Growth factor per step, a=1.0101 Probability of up ... are governed by a two-step binomial tree. ... that no-arbitrage arguments and risk-neutral valuation arguments ...