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FINA 410 (14)
Jean Mayer (14)
Lecture 5


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Course Code
FINA 410
Jean Mayer

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find more resources at CHAPTER 5 – OPTION PRICING THEORY AND MODELS Chapter 5: pp 87- 90 and 95-99  The value of any asset is derived from the PV of CF form that asset, this is the only exception to the rule and must have these 2 characteristics: o 1) the assets derive their value from other assets o 2) The CF’s o▯ the assets are co▯ti▯ge▯t o▯ the occurre▯ce of specific e▯e▯ts  USING DCF would understate their value. Basics of Option Pricing  Options gives you the right, not the obligation, to buy or sell underlying asset at a predetermined (strike) price o two positions in options: long (buyer) or short (seller)  American options can be excercised at any time, European options only at expiration o American options more valuable but also harder to value o The value of an option is determined by 6 variables relating to the underlying asset and financial markets: o 1) Current value of the underlying asset: o underlying increases → call increases, put decreases o 2) Volatility of the underlying asset: o volatility increases → call and put increase o 3)Dividends paid on the underlying asset: o dividends increase → underlying decreases → call decreases, put increases o 4) Strike price of the option: o strike increases → call decreases, put increases o 5) Time to expiration on the option: o time decreases → call and put decrease o 6) Riskless interest rate corresponding to life of the option: o interest increases → PV (strike) is cheaper → call increase and put decrease find more resources at find more resources at Black-Scholes Model  When the price process is continuous, the binomial model for pricing options converges to the Black-Scholes model: o S = Current value of the underlying asset o K = Strike price of the option o t = Life to expiration of the option o r = Riskless interest rate corresponding to the life of the option o σ = ▯olatility (standard deviation) in the log returns of the underlying asset  The value of a call is then: o Note that e–rt is the PV factor, and reflects the fact that the exercise price on the call option does not have to be paid until expiration.  N(d1 ) and N(d2 ) are cumulative standardized normal distribution probabilities  In approximate terms, N(d2 ) is the likelihood that an option will generate positive cash flows for its owner at exercise o (i.e., that S > K for the call and K > S for the put.  The portfolio that replicates the call option is created by: o buying N(d1 ) units of the underlying asset, and borrowing Ke–rtN(d2 ).  This portfolio ▯ill ha▯e the sa▯e CF’s as optio▯, a▯d thus the sa▯e ▯alue o N(d1), which is the number of units of the underlying asset that are needed to create the replicating portfolio, is the option's delta.  A note on estimating inputs:  Block scholes
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