1011260-Cor-13 - EquityDerivatives andRelatedProducts...

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Equity Derivatives  and Related Products Class 13: Volatility Derivatives / International Strategies / Financial Regulation Mark Zurack November 30, 2010
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1002220-MBA-11 2 Class Objectives To complete our discussion on Volatility Derivatives To discuss the role of EMU in the development of the European  Derivatives market To introduce Equity Derivatives transaction driven by withholding tax  issues To review the fall of Barings and how Derivatives Went Awry To show examples of how Equity Index Swaps are constructed in  Emerging Markets and how investors use Zero-Strike options to buy  stocks they cannot easily trade in the cash markets 1011260-Cor-13
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1002220-MBA-11 Pricing a Variance Swap: Capturing Realized Variance The price of a variance swap (variance strike) is based on the cost of  the dealer’s replicating portfolio   The dealer’s goal is to generate a replicating strategy to capture  realized variance The replicating strategy requires an options portfolio with constant  exposure to the realized variance of the underlying stock or index  under a wide set of circumstances (no jumps) Fair Variance  Strike  Cost of  Replicating  Portfolio  3 Source: Goldman Sachs Research 1011260-Cor-13
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1002220-MBA-11 The Replicating Portfolio:  A Single Option Won’t Do A single option is an imperfect vehicle for replicating variance since it’s  exposure to variance :   Varies as the stock price moves    Is largest when the option is at-the-money   Drops off rapidly as the stock price moves away from the option strike In order to hedge a variance swap, the dealer wants a portfolio whose  sensitivity to realized variance is independent of the stock price 20 40 60 80 100 120 140 160 180 Stock Price Variance exposure is greatest near the option strike Exposure drops off rapidly as stock moves away from the strike 4 Source: Goldman Sachs Research 1011260-Cor-13
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1002220-MBA-11 Constructing the Hedge: Building an Option  Portfolio with Constant Exposure to Variance A variance swap can be replicated with a portfolio of options that expire on  the same date as the swap. The replicating portfolio for the fair variance  strike at trade initiation: is a weighted average of put and calls over a wide range of strikes weights individual options by an amount inversely proportional to the square of  their strikes is better if more options strikes are used 20 60 100 140 180 Stock Price Strikes: 80, 100, 120 20 60 100 140 180 Stock Price equally weighted weight inversely proportional to square of strike Variance exposure of individual options  Variance exposure of portfolio A few options can approximately replicate over a limited range of strikes.   Traders are still exposed to large changes in the underlyer  Source: Goldman Sachs Research.
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This note was uploaded on 01/25/2011 for the course NBA 6940 at Cornell University (Engineering School).

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1011260-Cor-13 - EquityDerivatives andRelatedProducts...

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