# How would you price this kind of derivative?

I am somewhat familiar with options but am wondering how to price calls/puts on this one:

• European exercise
• "Jumps" in underlying may occur
• Takes physical delivery upon exercise (is this even relevant?)
• Fractional contracts not allowed (technically, though it should be arbitrage-free in reality)
• Underlying's value fluctuates in short-term (i.e. supply/demand) but generally decays over long-term

I am thinking you would input underlying price, volatility, time, and discount rate (decay), accepting some form of GBM. Not really sure though. Can someone please share 'what' this option is and the pricing models available? It seems something like a commodity or futures option but my knowledge in this arena is limited. I would like some formulas (or guidance towards) on how to price this. I have Excel, Matlab, and Maple at my disposal. Thanks in advance!

• Hi Tom, welcome to quant.SE! Thank you for asking your question here. – Bob Jansen Aug 13 '14 at 19:16

The other points of your question are rather of practical relevance only. The negative drift of the underlying is usually not important, because the pricing goes under the riskneutral measure $Q$.
• @Tom Yes that is what one would intuitively think, but as you may know also for the Black-Scholes model the asset drift is neutralized under the change of measure to $Q$, so the price is independent of the drift. You may think of it as a perfect market, where the negative drift is already priced in for both the stock and the put, then the value of the put comes solely from the asymmetric risk exposure it provides. – emcor Aug 13 '14 at 23:20