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jamesgin
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Joined: May 27th, 2011, 2:27 pm

implied vol near expiry

October 12th, 2011, 1:55 pm

Hi all,I'm using some historical option price data to explore hedging models - I solved BS for implied vol using newton raphson hoping to calculate greeks, however when time to expiry is small I'm experiencing problems calculating IV for ITM calls. Is there any way around this problem, or is there simply no solution for IV based on the traded prices I have?Thanks in advanceJames
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

implied vol near expiry

October 12th, 2011, 5:07 pm

An option price will correspond to a unique BS IV if and only if the price lies within the static arbitrage bounds. Bid/offer spreads and asynchronous option and stock price quotes may cause apparent violation of these bounds. Another problem is that the vega converges to a delta function (unlike the delta, which converges to a heaviside function -- confusing, isn't it?) at maturity, so the vega for an ITM option will become very small which may well screw up your NR. If this is the problem, you can get around it with using binary search (or another root finder that is not gradient based).
 
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Aaron
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Joined: July 23rd, 2001, 3:46 pm

implied vol near expiry

October 12th, 2011, 8:31 pm

Bearish is correct. First check if the option price is greater than its intrinsic value. If so, assign a Delta of 1 or -1 and zero for the other Greeks. There are other ways to deal with this, but this is the simplest.If the option price is greater than the intrinsic value but your algorithm is not coverging, or converges to a value you don't like, you could fix your algorithm as Bearish suggests. However it's likely that the result will not be meaningful. Time to expiry may not be accurate and bid/ask spreads plus exercise costs become important.
 
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jamesgin
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Joined: May 27th, 2011, 2:27 pm

implied vol near expiry

October 14th, 2011, 2:31 pm

Thanks for the help. The quick fix seems to have worked well.