Time Decay - Option Trading

Time Decay?

Many traders believe that the VIP calls lost money simply because of time decay. Time decay means that time has been subtracted from the life of the option and that the option must therefore be worth less money. However, that assumes that all other factors stay the same. We can use the Black-Scholes Model to see if time decay was the culprit. Figure 13 shows that if we use a volatility of 79.64% then the price of the call is $2.50, which was the market price at the time we considered buying the $33,375 call:

Thirteen days later, the stock rose to $34. Figure 14 shows the value of the $33,375 call thirteen days later (26 days to expiration instead of 39) would be $3.20 assuming that volatility remained constant at 79.64%:

So, the fact that time decayed by thirteen days was not the culprit of the loss on the VIP $33,375 call[1]. Had thirteen days passed and volatility remained con­stant, we would have been able to sell the call for $3.20 and gained a nice profit. Instead, we faced a loss with the call bidding only $1.80. Which volatil­ity is necessary to create a $1.80 bid price?

Figure 15 shows that an implied volatility of about 40% (39.81%) equates to a $1.80 call price. This shows that the reason the $33,375 call lost money was not because of time decay but rather that the implied volatility was cut in half; it fell from 80% to 40% in thirteen days.

The Black-Scholes Model allowed us to see the volatilities that the market was using to price the $33,375 call. Had we not used the model, all we would see is the $2.50 call price and have to make our decision based on our belief of the direction of the stock. But as we’ve seen, knowing the direction is not enough to profit on options. We must also know something about the volatility that the market is using to price the options. Because the market’s assessment of volatil­ity was so high, we were faced with a very large premium ($2.50 market price versus our estimate of $1.30). In order to overcome this large premium, the call option had a high-speed component. Had VIP moved from $31.41 to $34 the next day, we would expect the call to be profitable. But it took thirteen days to get there and that’s a different story.