Intermediate Investments F3031 Option Pricing There are two primary methods we will examine to determine how options are priced –Binomial Option Pricing –The Black – Scholes Option Pricing Model

Intermediate Investments F3032 Binomial Option Pricing Also known as Two-state option pricing Assume that a stock will end the period at one of two prices, but those are the only two outcomes that are possible

Intermediate Investments F3033 Binomial Option Pricing Example Consider the following –A stock sells for $100 –The price will either increase to $125 or decrease to $80 –Assume the current one period interest rate is 10% –A call option on the stock matures in exactly one year –The Exercise price on the option is $110 What is the value of the Option?

Intermediate Investments F3034 Binomial Option Pricing Example (cont) First, create a financial strategy that would replicate the payoff structure of the option –Use known variables, so a combination of buying the stock today and borrowing the PV of the minimum value of the stock in the future Find the Payoff of the strategy Value the call option based on the cost of the replication strategy

Intermediate Investments F3035 Creating a Hedge The Hedge Ratio – the ratio of the range of the values of the option to those of the stock across the two possible outcomes that makes the strategies’ payoffs equal The Perfect Hedge – is one that locks in the end of year payout regardless of the value of the stock The Hedge Ratio can be depicted as: C + - C - S + - S -

Intermediate Investments F3036 Key Takeaways 1.The Binomial model is a way to determine that options are fairly valued 2.With significantly more mathematics you can look at multiple periods and outcomes 3.The Binomial model is very flexible 4.It is one of the most widely used techniques on Wall Street

Intermediate Investments F3037 Put – Call Parity For European style Puts and Calls, Put prices can be derived from the prices of Call options –Both the Put and the Call must have the same Exercise Price –Both must also have the same expiration date –We will assume that we are buying a Call option and writing a Put option

Intermediate Investments F3038 Put – Call Parity (cont) You can replicate the position by borrowing money at the risk free rate and adding that inflow to a stock portfolio ( a long Call/ short Put position) –Cash outlay to establish the option position is C – P –Cash outlay for the ‘levered equity position’ is S 0 – X/(1+R f ) T –So C – P = S 0 – X/(1+R f ) T And –C = P + S 0 – X/(1+R f ) T –P = C - S 0 + X/(1+R f ) T

Intermediate Investments F3039 Put – Call Parity (cont) This is true for European Options assuming the stock pays no dividends If there are dividends, the equation is P = C - S 0 + X/(1+R f ) T + PV (dividends)

Intermediate Investments F30310 Put – Call Parity Example Assume the following –A stock is currently selling for $100 share –Put options have a price of $2, an exercise price of $90 and 3 months to maturity –The risk free rate is 5% –What should be the value of the Call option? –If the market value of the Call option is actually $12, does an arbitrage opportunity exist and if so, how?