FIN 3506 Lecture Notes - Lecture 9: Rational Pricing, Risk-Free Interest Rate, Put Option

56 views6 pages

bronzeturtle979

6 Oct 2016

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

Document Summary

The following is a little different approach than that of you text but results in the same answers. The equations present in the text solve the general condition. Let us assume that a portfolio consisting of going long the stock and shorting the risk free bond can be made to replicate the pay out of the option that we are trying to price. To show this let us assume that we are trying to price an option that has a strike price of. 50 and expiration at the end of one period. The current price of the underlying asset is. 50 and we have determined at the end of the next period the stock price will either rise to 60 or fall to 40. Let us further assume that the price of a risk free bond is currently b and currently has an interest rate of 3% for the period in question.

Related Questions

(Binomial Option Pricing Model) Consider a binomial world in which the current stock
price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4
percent. Assume a one-period world. Answer questions below about a call with an exercise
price of 80.
a. What would be the call's price if the stock goes up?
b. What would be the call's price if the stock goes down?
c. What is the hedge ratio?
d. What is the theoretical value of the call?

Question 3

Consider a stock currently worth $80 (S = 80) that can go up or down by 25 percent per period. The exercise price is $80 (X = $80) and the risk-free rate is 5 percent (r = .05). The option will expire at the next period (t = 1). You try to find a theoretically fair value of the call using a one-period binomial option pricing model. Answer the following questions. (Hint: See Ch 16 Teaching Notes and Excel Spreadsheet)

Compute the u and d in the binomial option pricing model such that the stock prices at the next period are Su and Sd.

What are two possible stock prices at the next period?

What are the intrinsic values at expiration of a European call option if the stock goes up and down?

Compute two values at expiration of a European call option (C_u and C_d)?

Compute the binomial probability (p)?

Find the theoretical fair value of the call option today using the one-period binomial pricing model.

Compute the riskless hedge ratio (h).

In order to construct a riskless hedge position by buying stocks and selling 1,000 calls using the riskless hedge ratio (h). How many stocks should you buy at what price? At what price should you sell the calls?

Compute the initial value of the riskless hedge position (V₀).

Compute the market values of the riskless hedge position at the next period if the stock goes up (V_u) and goes down (V_d).

Find the rate of return on the riskless hedge position (R).

apricothippopotamus885

Consider a stock currently worth $80 (S = 80) that can go up or down by 25 percent per period. The exercise price is $80 (X = $80) and the risk-free rate is 5 percent (r = .05). The option will expire at the end of the third period (t = 3). You try to find a theoretically fair value of the put option using a three-period binomial option pricing model. Answer the following questions.

t = 0	t = 1	t = 2


		Suu = (c)
	Su = (a)
S = $80		Sud = (d)
	Sd = (b)
		Sdd = (e)



		P_uu = (f)
	P_u = (i)
P = (k)		P_ud = (g)
	P_d = (j)
		P_dd = (h)

a) What are three possible stock prices at time t = 2 (c, d, and e)?

b) Compute three values at time t = 2 of European put options. (P_uu, P_ud, and P_dd)

c) Compute two values at time t = 1 of a European put options (P_u and P_d).

d) Find the theoretical fair value of the put option today (P).

e) Compute the riskless hedge ratio (h).

f) Construct a riskless hedge position with stocks and 1,000 put options at the theoretically fair value using the riskless hedge ratio (h).

taupecamel175

FIN 3506 Lecture Notes - Lecture 9: Rational Pricing, Risk-Free Interest Rate, Put Option

Document Summary

Get access

Related Documents

FIN 3506 Lecture 12: Notes_12_Derivatives

FIN 3506 Lecture Notes - Lecture 10: Stochastic Differential Equation, Normal Distribution, Risk-Free Interest Rate

FIN 3506 Lecture Notes - Lecture 11: Risk-Free Interest Rate, Delta Gamma, Stochastic Differential Equation

Related Questions