FINS3635 Week 12 - Greek letters (3)

FINS3635 Week 12 - Greek letters (3) - The Greek Letters(Ch...

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1 The Greek Letters (Ch. 18) Management of Market Risk Delta Gamma V FINS 3635 week 12 1 Vega Other Greek Letters Theta Rho Example (Hull 18.1) A bank has sold (for $300,000) a European call option on 100,000 shares of a non-dividend paying stock S 0 = 49, X = 50, r = 5%, = 20%, FINS 3635 week 12 2 T = 20 weeks The Black-Scholes value of the option is $240,000 How does the bank hedge its risk? In, at or out of the money? What risk does the bank face? Naked & Covered Positions (Hull 18.2) Naked position Take no action - how much could the bank lose? Covered position FINS 3635 week 12 3 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 ?
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2 Stop-Loss Strategy (Hull 18.3) Buy 100,000 shares as soon as price reaches $50 Sell 100,000 shares as soon as price falls below $50 FINS 3635 week 12 4 This simple hedging strategy does not work well. Why not? 1) transaction costs 2) how do you decide whether the price will go up or down or will continue? 3) Buy high and sell low More Sophisticated Hedging Strategies Try to hedge option price risk How? Look for the factors that have effects on the option price FINS 3635 week 12 5 Figure out relation between these factors and option price Measure how sensitive of the option price is to the changes in value of these factors Come up a strategy to reduce the sensitivity, i.e., risk-free (risk neutral) portfolio Determinants of option prices Five factors determine option prices: Price of the underlying S Exercise price X Volatility of returns of S σ FINS 3635 week 12 6 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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