Enhanced Numerical method for barrier option pricing

rakeshkashyap · January 4th, 2006, 8:18 am

hi, I'm using Implied Trinomial Tree model to price a barrier option. The problem is when the barrier falls between the nodes. In the case of knock-out it is giving me desired result but how to do the interpolation in Knock-in options, which all nodes we need to overwrite and how?The method is described in Derman kani's paper but i'm not able to find any example for knock-in option. every where it is explained for knock-out option. so can you please suggest me any good reference.rox

NamelessWonder · January 4th, 2006, 4:16 pm

You use the In-out parity result to get the Knock-in option value. So do the knock-out pricing. Do the vanilla pricing. And then add 2+ 2 to get 48.

spursfan · January 5th, 2006, 9:13 am

Google for "Barrier Put-Call Transformations" by the esteemed Collector of this parish

Keanu · January 5th, 2006, 1:43 pm

A trinomial tree can be adjusted to barriers:See:P. Ritchken (1995)_On pricing of barrier Option. Journal of Derivatives, pages 19-28, Winter 1995Check out this online-pricer:http://www.geocities.com/harrytan06/Tree/Ritchken.html A knock in option can be replicated by a portfolio of the corrosponding vanilla optionand a knock-out option. Something like:Knock-in-Call = Vanilla-Call - Knock_out_CallThink about it.

Cuchulainn · January 5th, 2006, 2:01 pm

QuoteOriginally posted by: KeanuKnock-in-Call = Vanilla-Call - Knock_out_CallThink about it.Are there any restrictions? Can we have discrete monitoring and/or exponential barriers? Or in these cases do we have to solve 2 separate problems?Is delta (ki) = delta(van) - delta(ko)?

Keanu · January 9th, 2006, 11:23 am

I would call this identity the "In and Out Parity":(S(T)-K)^+ = (S(T)-K)^+ * 1_{S(t)>b(t) for all t in [0,T] + (S(T)-K)^+ * 1_{S(t)<b(t) for a t in [0,T]}in other words:Vanilla Call = Call Down-Out + Call Down-InIt holds also for time-dependent barriers and also the deltas match.It works as long the characteristic functions add up to one, so it holds alsowith discrete-monitoring.

rakeshkashyap · January 10th, 2006, 8:35 am

Thanks for your valuable suggesions..... i got it and is resolved now...... i didnt use the put-call parity.... i got the values for knock-In and knock-out separately.Thanks....

cosmologist · January 14th, 2006, 5:43 am

QuoteOriginally posted by: rakeshkashyapThanks for your valuable suggesions..... i got it and is resolved now...... i didnt use the put-call parity.... i got the values for knock-In and knock-out separately.Thanks....Hull tells you about the parity, it may be a grade ii book,still it is useful. Why the quadrature method have not been mentioned here?