Multifactor Models

Regression based multi factor models may not really work when the distributions of the variables are not normal. But I have been thinking that this can be rectified using kernel or copular based transformation of the variables.

Suminda Sirinath Salpitkorala Dharmasena

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Etreme Options - Zero Strike options

A long position is equivalent to a zero strike call or a zero strike put plus a long call. The long call is is a zero strike call. A zero price put is a short at zero and a call at zero. Short at zero is equalant to a short long call at zero. ;-)

 

Option Abitrage

If you can find an put option at a higher strike price such that the call at this price plus the interest in the short position on the stock up to expiration of the stock is less than the put's extrinsic value then it is a arbitrage opportunity.

 

If the sum of extrinsic values of two out of the money call and put options above and below the current stock should be the same as the sum of two options in the money at the respective prices. Otherwise there is a arbitrage opportunity, if the extrinsic value of the in the money portfolio is greater.

 

A long position is equivalent to a zero strike call or a zero strike put plus a long call.

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Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein



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The Black Scholes and the Greeks

These values would be less valid if the distance between the lower and higher strike is large percentage of the stock price. E.g. the stock is trading at USD 1.50 and the lower and higher strikes are 1 and 2 then the option may be too deep in or out of the money to have BS working correctly. If you look at the Delta or the theoretical Greeks values, they are meaningless.

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Thanking you.
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Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

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Greeks Estimated at a Point and Point Alone

In the real world fiance is not continuous time fiance. Therefore looking at the Greeks at a point of time would not be ideal. With discrete movements of stock price, interest rates and even historic volatility, the actual impact of the Greeks to a model would be different than anticipated.

 

Ideally to overcome this situation:

1. The Greeks should be empirically estimated. Intra day data can be used to estimate delta, gamma assuming time to expiration and volatility does not change much. In the case of volatility it is worth while to see that the implied volatilises also does not change much from previous to ensure that this assumption holds
2. Based on expected distribution of discrete market events and calculate the expected dicretised version of the Greek. This is needed due to the instability of the Greeks due to its payoff structure, especially when considering exotics.

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Thanking you.

Best regards,

Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

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The Thing with Black Scholes

Black Scholes (http://en.wikipedia.org/wiki/Black-Scholes) is generally not perfect. This imperfection is greater when either absolute of d1 or d2 is large. As a rule of thumb I check if the value is greater than 3, i.e. 3 SD. When d1 and d2 becomes large, i.e., when calculating the probability of the tails of the cumulative started normal distribution, the equation becomes more and more sensitive to these parameters and slight variation can produce erratic results. Also I presume the numeric error of calculating the cumulative standard normal would be large in the tails.

 

Be very of the Greeks (http://en.wikipedia.org/wiki/The_Greeks) when d1 and d2 are large. They would be imperfect and meaningless.

 

This error would be predominate in options deep in our out of the money and close to expiration. This is when d1 and d2 becomes absolutely large.

 

I guess the skew in the implied volatility surface is an attempt to correct this imperfection by the market participants. Though it has been generally termed as crash phobia after Black Monday, I guess this might be a attempt to correct and work around the imperfections in the Black Scholes equation itself through experience and learning its limitation which most probably felt during the market crash.
--
Thanking you.
Best regards,
Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

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Go High Gamma

Hello there!

What are the implications of being high is Gamma:

• Options are near the money
• Time to expiration may be low
• At the money option near expiration has a high level of gamma

When maintaining a high gamma position you should be vary of the effects of

• Theta - the decay of your portfolio value. This would be paramount if the option are near the money.
• Time to expiration would be low, thus the implied volatility would be high

Of course any hedging error would be favourable therefore delta instability or the instability of the delta hedge will not count. Where as if it is negative Gamma it would be unfavourable.

 

Thanking you.

Best regards,

Suminda Sirinath Salpitikorala Dharmasena B.Sc. (Hon.) Comp. & I.S., Lon.

The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honours the servant and has forgotten the gift. - Albert Einstein

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Suminda Sirinath Salpitikorala Dharmasena

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Hedging Error and Discretising Continuous Time Models

Hi,

Hedging error need not always need to be minimized. If it is favorable, it is advantages to let it be large as possible. The discretising of a continuous time model should be done so that the hedging error would be most favorable subjected to trading costs and other considerations. This would be a additional source of returns beyond what the model specifies.

Suminda Sirinath Salpitikorala Dharmasena