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EFN412 Advanced Managerial Finance School of Economics and Finance, QUT Topic 10 Topic: 10. Risk Management - Options Required Reading: PBEHP 10 th edition Chapter 18 or PBEHP 9 th edition Chapter 19 Refer to the Blackboard site for the Cumulative Normal Distribution (area under the normal curve) that will be supplied with the examination paper. A copy is also provided at the end of this document. Complementary Reading: RTCWJ 4 th edition, Ch.20 or RTCWJ 3 rd edition Ch.21 Learning Objectives: o Understand Options. o Understand how options differ from forwards/futures. o Understand option profit & payoff diagrams. o Understand the determinants of option prices. o Calculate the value of a call option. o Understand the concept of put-call parity. o Calculate put options using put-call parity . Tutorial Activity: Question 17 Part (d) Page 1

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OPTIONS – ADDITIONAL NOTES The Black-Scholes Option Pricing Model (THESE FORMULA WILL BE GIVEN IN THE EXAM) Where: c = the value/premium of the call option S = the current share price X = the exercise price R f = riskfree rate of interest σ 2 = the variance of the share's rate of return T = the time to expiry of the option (as a fraction of a year eg. 0.5) N(d) = cumulative normal density function e = natural log base = 2.71828 To convert d 1 and d 2 to their equivalent N(d 1 ) and N(d 2 ) use the cumulative normal distribution table from the Blackboard site, or PBEHP 10 th edition pp.786-787 or PBEHP 9 th edition pp.818-819 or RTCWJ 4 th edition p.862 or RTCWJ 3 rd edition p.858 or the NORMSDIST() function from an Excel spreadsheet. Page 2 c = S.N(d ) - X.e .N(d ) 1 -R T 2 f T )T + R ( + X S = d 2 f 1 σ σ 2 1 ln T - d = d 1 2 σ
Put-Call Parity To demonstrate put-call parity, we will set up two portfolios of investments: A and B. Portfolio A The investor buys a put option with an exercise price of X, and also buys a share in the company on which the put is written. The total cost of this investment is p + S. Portfolio B The investor buys a call option with an exercise price of X, and invests a sum (Xe -RfT ) in government bonds. The total cost of this investment is c + Xe -RfT . It can be shown that these two portfolios will have exactly the same payoffs, no matter which way the share price moves. Payoffs at maturity from Portfolio A If S maturity > X: Shares = S mat Put = 0 put option is worthless and we won't exercise. Total S mat If S maturity < X: Shares = S mat Put = X - S mat we will exercise put option at a profit. Total X Payoffs at maturity from Portfolio B If S maturity > X: Call = S mat - Xwill exercise our call option at a profit. Bonds = X Xe -RfT will mature with a value of X Total S mat If S maturity < X: Call = 0 call option is worthless and won't be exercised Bonds = X Total X From the above, we see that no matter what happens with the share price, the payoffs from both portfolios are the same. Because the two investments have the same payoffs, they must have the same costs. That is, the initial investments must be identical. Arbitrage – one of the three ideas of finance – see RTCWJ 4 th edition p.149 or RTCWJ 3 rd edition p. 144. Hence: p + S = c

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