Time value of deeply ITM options

[andy orodo]

Hi,

The time value of long term deeply in-the-money put options........... how significant is the time value expected to be? Am I correct in thinking that the volatility skew would result in an increase in the option implied vol, and that this would increase the time value? Or would you expect the time value to become less significant the further away from the ATM postion it moves? What is more significant?

Thanks,
Andy

 

[manish.rex]

Hi,

The time value of long term deeply in-the-money put options........... how significant is the time value expected to be? Am I correct in thinking that the volatility skew would result in an increase in the option implied vol, and that this would increase the time value? Or would you expect the time value to become less significant the further away from the ATM postion it moves? What is more significant?

Thanks,
Andy

The time value for deeply in the money put will not be much significant, in fact as the time passes, the value of the option will increase, which also implies that as volatility decreases the option value will increase from its current position=> decrease in volatility will lead to incrase in option value.

The logic behind this is that the option is already in the money. And it may also be the case that the option cant move any further in the money (stock price has already hit value of 0).

Hence any increase in the time to expiry of option will imply increase in likelihood of stock price moving up towards the strike=> decrease in the option value.

Likewise, and increase in the volaitility of the underlying's price will imply increasing the odds of the value hitting the strike, thus lower option's value.

The best think to happen is : either time to maturity shrinks to 0 for such an option (in the money), or volaitility to drop to 0 (price of stock fixed at it's current value). Any thing otherwise is only going to cause the option proce to fall.

Hope this helps

 

[andy orodo]

The time value for deeply in the money put will not be much significant, in fact as the time passes, the value of the option will increase, which also implies that as volatility decreases the option value will increase from its current position=> decrease in volatility will lead to incrase in option value.

The logic behind this is that the option is already in the money. And it may also be the case that the option cant move any further in the money (stock price has already hit value of 0).

Hence any increase in the time to expiry of option will imply increase in likelihood of stock price moving up towards the strike=> decrease in the option value.

Likewise, and increase in the volaitility of the underlying's price will imply increasing the odds of the value hitting the strike, thus lower option's value.

The best think to happen is : either time to maturity shrinks to 0 for such an option (in the money), or volaitility to drop to 0 (price of stock fixed at it's current value). Any thing otherwise is only going to cause the option proce to fall.

Hope this helps

Thanks for this.

Consider a put option with strike 100 and stock price 150 i.e. deeply in-the-money. The majority of the option price is expected to be made of the intrinsic value of 50. But, should the stock price move +/- 10, the impact on the change in payout would be the same as that of the same movement if the stock price was 110. Hence I would expect volatility to still be just as significant assumption if the price were to move in-the-money, ignoring the differences in instrinsic value.

In fact, because of the volatility smile, if I had an at-the-money put optionand it moved deeply in-the-money, then I would have expected both the intrinsic and the time value of the otpion to have increased.

Is there a flaw in my logic here? Thanks for your help.

 

[manish.rex]

Thanks for this.

Consider a put option with strike 100 and stock price 150 i.e. deeply in-the-money. The majority of the option price is expected to be made of the intrinsic value of 50. But, should the stock price move +/- 10, the impact on the change in payout would be the same as that of the same movement if the stock price was 110. Hence I would expect volatility to still be just as significant assumption if the price were to move in-the-money, ignoring the differences in instrinsic value.

In fact, because of the volatility smile, if I had an at-the-money put optionand it moved deeply in-the-money, then I would have expected both the intrinsic and the time value of the otpion to have increased.

Is there a flaw in my logic here? Thanks for your help.

For an option , the effect of time value and volatility value of money imply the same thing (higher time => higher chances of stock becoming in the money and higher volatility => higher chances of stock becoming in the money .

Having said that , if the option is already deeply in the money, a higher volatiliy , specially for a put option, will imply that the option may go out of money with higher likelihood. This is because downside movement is capped (stock price falling to 0 and option payoff max out at K).

If one remembers the intrinsic value and total value of option graph from Hull, the difference between the two(time value) is the highest just when the stock price is equal to the strike price. before and after that, the farther away the price from K, the lower the difference.Hence, as a % of total value, time value will be a decreasing function of the distance to strike, holding volatility and time to maturity constant.