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Lecture 12 The Greeks - Lecture 12(Ch17 The Greeks...

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Lecture 12: (Ch17) The Greeks Management of Market Risk o Delta o Gamma o Vega Other Greek Letters o Theta o Rho Example (Hull 17.1) A bank has sold (for $300,000) a European call option on 100,000 shares of a non- dividend paying stock S0 = 49, X = 50, r = 5%, σ = 20%, T = 20 weeks. The Black- Scholes value of the option is $240,000 o How does the bank hedge its risk? o In, at or out of the money? o What risk does the bank face? Naked & Covered Positions Naked position o Take no action How much could the bank lose? Covered position o Buy 100,000 shares today What is wrong with this strategy? Both strategies leave the bank exposed to significant risk. When does the bank ‘need’ the underlying? Stop-Loss Strategy (Hull 17.3) Buy 100,000 shares as soon as price reaches $50
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Sell 100,000 shares as soon as price falls below $50 This simple hedging strategy does not work well. o Why not? Transaction costs How do you decide whether the price will go up or down or will continue? Buy high and sell low More Sophisticated Hedging Strategies Try to hedge option price risk How? o Look for the factors that have effects on the option price o Figure out relation between these factors and option price o Measure how sensitive of the option price is to the changes in value of these factors o Come up a strategy to reduce the sensitivity, i.e., risk-free (risk neutral) portfolio Five factors determine option prices: Price of the underlying S Exercise price X Volatility of returns of S σ time to maturity of option T or (T-t) risk free rate r What is the effect of a change of one of these factors on the option price holding all others constant?
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