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60202
Topic Author
Posts: 35
Joined: August 27th, 2012, 11:34 pm

### How do I adjust the BSM Model to price binary options?

Hello,

I'm trying to figure out a way to price binary options where the payoff is either 0 or a fixed value.  I did some quick Googling and seems like people do use the BSM model to price binary options but I'm not seeing any instructions on how to adapt it.

Any suggestions?

Thanks!

Paul
Posts: 8589
Joined: July 20th, 2001, 3:28 pm

### Re: How do I adjust the BSM Model to price binary options?

60202
Topic Author
Posts: 35
Joined: August 27th, 2012, 11:34 pm

### Re: How do I adjust the BSM Model to price binary options?

oh wow, didn't know this site has a wiki.  Thakns!

so there's no need for the d1 term at all for pricing binary options?

bearish
Posts: 3681
Joined: February 3rd, 2011, 2:19 pm

### Re: How do I adjust the BSM Model to price binary options?

60202 wrote:
oh wow, didn't know this site has a wiki.  Thakns!

so there's no need for the d1 term at all for pricing binary options?

It depends on the option. If the option specifies that you receive the underlying asset if its value is above (or, alternatively, below) the strike price, then you need d1 but not d2.

60202
Topic Author
Posts: 35
Joined: August 27th, 2012, 11:34 pm

### Re: How do I adjust the BSM Model to price binary options?

thank you. the one i'm trying to price is cash settled.

EdwinB
Posts: 8
Joined: February 12th, 2018, 10:58 pm

### Re: How do I adjust the BSM Model to price binary options?

Although it seems easy The Feynman-Kac formula says that the solution to this type of PDE, when discounted appropriately, is actually a martingale. Thus the option price is the expected value of the discounted payoff of the option. Computing the option price via this expectation is the risk neutrality approach and can be done without knowledge of PDEs, it is not easy what you want. Good luck!