FINA 412 Lecture Notes - Lecture 10: Option Style

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amberfrog615

1 May 2015

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Pricing american options (cid:15) in this chapter we will price american options written on the stocks that pay and do not pay dividends as well american options on indexes. Pricing will be carried by using binomial trees. (cid:15) first, we quickly review a binomial model for no{dividend stock. S(i; j) = s0uidi(cid:0)j j = 0; 1; :::; i (cid:15) notice that the stock tree is recombining in the sense that up{down movement results in the same price as down{up movement for any node on the tree. Moreover, for a given number of up movements the stock price is brought to the original value by the same number of down movements independently from the orders of movements. She makes the best decision implying that the value (price) of a put option in a given node n is n = maxf(k (cid:0) sn)+; png;

Related Questions

Find the current price of a one-year, $110-strike American put option on a non-dividend-paying stock whose current price is S(0)=$100. Assume that the continuously compounded interest rate equals r=0.08. Use a two-period binomial tree with u=1.2 and d=0.8 to calculate the price of the put option.

taupecaribou20

16) Which of the following statements is correct about the early exercise of American options?

		a) It is always optimal to exercise an American call option on a non-dividend-paying stock before the expiration date.
		b) It can be optimal to exercise an American put option on a non-dividend-paying stock early.
		c) It can be optimal to exercise an American call option on a non-dividend-paying stock early.
		d) It is never optimal to exercise an American put option on a non-dividend-paying stock before the expiration date.

champagnewhale873

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

FINA 412 Lecture Notes - Lecture 10: Option Style

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