Pricing an option with payoff at-the-money?

[benzbubblecat]

I don't want to post this in the pricing section because it's a bit silly.

Lets say that there exists a hypothetical stock option which is neither a call nor a put. You buy it at-the-money and you get a constant payoff if it finishes exactly at-the-money (or close to it) at expiration. The farther away from the strike price the asset is at expiration, the more you lose at an increasing rate.

Could one price this option, given a specific payout and time til expiry? I'm specifically interested in whether you could price it with Monte Carlo or binomial.

 

[AndrewChang]

I don't want to post this in the pricing section because it's a bit silly.

Lets say that there exists a hypothetical stock option which is neither a call nor a put. You buy it at-the-money and you get a constant payoff if it finishes exactly at-the-money (or close to it) at expiration. The farther away from the strike price the asset is at expiration, the more you lose at an increasing rate.

Could one price this option, given a specific payout and time til expiry? I'm specifically interested in whether you could price it with Monte Carlo or binomial.

this is just a short straddle...

 

[aaronhotchner]

this is just a short straddle...

Well, not quite. He said that you lose money at an increasing rate w.r.t. the asset price. I don't know that he actually meant to say that, but...

In any event, yeah, you can price it with a binomial tree, why not? Monte Carlo would probably be faster if you don't already have the tree model set up.

 

[AndrewChang]

Well, not quite. He said that you lose money at an increasing rate w.r.t. the asset price. I don't know that he actually meant to say that, but...

In any event, yeah, you can price it with a binomial tree, why not? Monte Carlo would probably be faster if you don't already have the tree model set up.

don't need MC to price this, there are market prices. can just sell all out of the money puts until at the money, and sell all out of the money calls until at the money. the following paper by peter carr shows how you can replicate any twice differentiable payoff

http://www.math.nyu.edu/research/carrp/papers/pdf/statichedge22.pdf