ASM p.25 #2.8

[wbuck]

I am having trouble understanding problem 2.8 on Page 25 of the ASM MFE manual. The problem gives the following put option prices:
Strike price ..... Option price
50 ................ 5
65 ................ 12
75 ................ 15

And asks us to exploit the mispricing. The solution originally says that the 65-strike option is underpriced, and the errata say that it is actually overpriced. But as I understand it, the price curve for put options increases as strike price increases, but gets flatter as the strike price gets higher. That means the price for a 65-strike option should be greater than the price indicated by linearly interpolating between the 50-strike option and the 75-strike option. The linear interpolation indicates a price of 11, so the 65-strike option should have a price greater than 11. It does. So why is it overpriced?

Thanks for any help anyone can offer.

[Boertjie]

Originally Posted by wbuck

That means the price for a 65-strike option should be greater than the price indicated by linearly interpolating between the 50-strike option and the 75-strike option.

I believe this is: "...should be less than the price indicated by..."

[Abraham Weishaus]

Originally Posted by Boertjie

I believe this is: "...should be less than the price indicated by..."

Correct. The slope gets steeper and steeper, so if it went up 7/15 from 50 to 65 (5-->12), it should go up at least (7/15) (75-65) from 65 to 75, which makes the minimum price of strike 75 more than 16.

[wbuck]

Thank you! This makes more sense now. I had been thinking that the put premium curve got flatter and flatter (like the square-root function), but now I see the errata note that it actually gets steeper and steeper, which makes much more sense.