Options

Options Financial Options There are Options and Options - Financial options - Real options

Options Financial Options A financial option gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price at some future date. Puts Calls Strike price/Exercise price American/European

Table 20.1 Option Quotes for Amazon.com Stock

Options Financial Options Option Pricing Binomial - Two state single period - Law of one price - Replicating portfolio Call option, SP 50, No dividend, Stock will either rise by 10 or fall by 10 Risk free rate is 6%

Options Financial Options/Pricing 0 1 Stock Bond Call 60 1.06 max (60-50,0) = 10 Stock 50 Bond 1 40 1.06 max (40 -50,0) = 0 60 = up and 40 = down S = Share price and t = number of shares and B = investment in the bond. SP = 50

Options Financial Options/Pricing Value of portfolio containing the stock and the bond must = the value of the portfolio in each state. 60St + 1.06B = 10 40St + 1.06B = 0 So St = .5 And B = - 18.8679 60 x .5 - 1.06 x 18.8679 = 10 40 x .5 – 1.06 x 18.8679 = 0

Options Financial Options/Pricing Generalising we get St = Cu – Cd and B = Cd – Sdt Su – Sd 1+rf This gives us the replicable portfolio The Call option price then follows C = St + B or 50x.5 – 18.8679(1) = 6.13

Options Financial Options/Pricing But what about multi period models? Strike price of 50, Rf = 6% 0 1 2 Periods 60 50 40 40 30 20

Options Financial Options/Pricing We start at the end and work back 1 2 60 Max(60 -50,0) = 10 50 40 Max 40 -50,0) = 0 This is the same as before therefore St = .5 and B = -18. 87 and the call value at time 1 is 6.13

Options Financial Options/Pricing What if share dropped to 30 in the next period (period 1)? 40 Max (40 – 50, 0) = 0 30 20 Max (30 – 50, 0) = 0 The option is worthless in both states so no portfolio value

Options Financial Options/Pricing Now move back a period 0 1 Stock Call 50 6.13 40 30 0 Now work out replicating portfolio at time 0 St = Cu – Cd = 6.13 – 0 = 0.3065 Su – Sd 50 – 30 B = Cd – Sdt = 0 - 30(0.3065) = - 8.67 1 + rf 1.06

Options Financial Options/Pricing So the Call value at Time 0 is C = St + B = 40(0.3065) +(-) 8.67 = 3.59

Options Financial Options/Pricing For European options if we let each period shrink to ‘zero’ and have an infinite number of periods then we may use the Black-Scholes formula to calculate the binomial pricing………….. but we won’t But remember the important factors in the pricing

Options Financial Options/Pricing The strike price The stock price The exercise date The risk free interest rate The volatility

Options Real Options And there are Real Options The right to take a particular business decision e.g. a capital investment decision. Main distinction is that the asset is normally not traded

Options Real Options Until now we have considered a stream of cash flows during the project, starting from today, to determine the NPV But what about alternatives such as delaying the start or abandoning the project after a while?

Options Real Options To analyse the alternatives we need Decision Trees A graphical representation of future decisions and uncertainty resolution (B & DeM)

Options Real Options Meet (re meet) Megan Goes to markets Sells, average profit 1,100 Costs of Booth 500, in advance profit 1,100 – 500 = 600 Go to meet Stay at home

Options Real Options Now add some uncertainty If it rains (25% chance) she will make a loss = -100 If it is sunny her profit is higher = 1,500

Options Real Options 1,500 sunshine 75% Go to meet Rain 25% - 100 - 500 - 100 Stay at home Decision node Information node

Options Real Options Go to meet or not? Go to meet Stay at home 1,500 Sunshine 75% Stay at home Pay for booth - 500 Rain 25% Go to meet -100 Don’t pay for booth Stay at home

Options Real Options So what is the ‘value’ of this real option to Megan? Expected profit without choice i.e. go to meet regardless = 1,500 x .75 +-100 x .25 = 1,100 Expected profit with choice = 1,500 x .75 = 1,125 So choice/option worth 25

Options Real Options Should Megan pay for the booth? Expected profit will be 1125 -500 = 625 So Yes

Options Real Options When else may they be used? Option to delay Invest now only where NPV is substantially greater than zero But What are costs of delay? What is volatility? What are costs of investment?

Options Real Options Option to Grow Option to Expand Option to Abandon Option to Prepay