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Unformatted text preview: rred in the option (stock). B UTTERFLY SPREAD Investors may also form a spread position by combining options of different series but of the same class, where some are bought and others are sold. Normal butterfly position will involve 1 long LEPO and 1 long HEPO with 2 short middle exercise price options, Initial Payoff = CL – 2CM + CH Final Payoff = Max {S* – XL, 0} - 2 Max {S* – XM, 0} + Max {S* – XH, 0} Profit and Loss = [Max {S* – XL, 0} - 2 Max {S* – XM, 0} + Max {S* – XH, 0}] – [CL – 2CM + CH] 15 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 In summary, a butterfly spread: A normal butterfly spread has symmetric payoff and P/L patters A normal butterfly spread has positive values when S* falls between the lowest and highest exercise prices, but no value otherwise Investors adopt position in anticipation of narrow sideway stock price movements, close to the middle exercise price Two breakeven points – between XL and XM, and between XM and XH Maximum profit is reached when S* = XM The potential loss is limited to the initial payoff, where S*<XL and S>XH 16 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 L ECTURE 11 – T HE BLACK SCHOLES OPTION PRICING MODEL (BSOPM) B ACKGROUND READING The BSOP Formula for a European call option written on a non-dividend paying stock is defined as: C = SN(d1) - Xe-rt N(d2) where: C = current price of a call (as suggested by the model). As the model price may differ from the actual market price, small letter ‘c’ is used to denote market price hereafter. S = current stock price d1, d2 = number of standard deviations away from the mean of a unit normal distribution with a mean of 0 and standard deviation of 1 ()( ) √ √ N(x) = cumulative probability of observing a value that is equal to or less than x under the unit normal distribution X = option exercise price r = annualised continuously compounded risk-free rate t = time to expiration in years σ = annualised standard deviation of continuously compounded stock...
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