Time to expiration and European Puts

CFA Level I Derivatives
#1

Hello All,

I can’t understand that for European puts, it’s uncertain whether shorter term puts will be worth more than longer term puts. Can someone please explain this? Schweser, unfortunately, has dedicated one sentence, and curriculum has dedicated one paragraph. I googled this a bit, but I was completely lost.

I would appreciate any help.

Thanks in advance.

#2

In most cases, the longer the time to expiry, the higher the put price. But not in all cases.

Imagine a far in-the-money put: the price of the underlying is near zero. As it can’t go below zero, if you wait around it’s a lot more likely to go up than down (making your put less valuable), so the time value is, in fact, negative. In that case, the shorter the time to expiry, the higher the put price (as the price converges to intrinsic value at expiry).

#3

Hello S2000magician,

Thank you for your response. I thought about your response for two days, but I couldn’t fully get it. I initially thought that Black-Scholes Model and the concept of time value is in L2. I am not quite comfortable with these concepts because I don’t have CFAL2 books. Do you mind giving me a quick example so that I can register this concept to my memory?

Thanks in advance.

#4

Unfortunately, I don’t know how to post screen shots of Excel here.

If you have a European put option on a stock with:

  • Strike price = $250
  • Annual effective risk-free rate = 0.5%
  • Time to expiration = 3 months (0.25 years)
  • Annual standard deviation of the stock’s returns = 30%

Using the Black-Scholes-Merton model, if the spot price is above $186.33, the time value is positive, but if the spot price is below $186.33, the time value is negative. For example, if the spot price is $150, then the option price is $99.69, the intrinsic value is $100.00, so the time value is -$0.31.

#5

I’m not sure if others would agree with this but my immediate thought is that if expectations for short term volatility are extremely high relative to expectations for longer term volatility this may cause the price of a Put for the front month to garner a higher premium than a Put with the same Strike Price for the following month (e.g., earnings announcements, etc.)

#6

While that’s certainly true theoretically, I’m not sure it plays out often (if at all) in practice.