Hello,I am interested in getting some intuition about why allowing for transaction costs in option pricing is important and the impact of such costs in options valuation formulas.As a starting point I focused on Leland (1985) model as explained in Wilmott book. I do not quite get Wilmott book intuition for the importance of model and interpretation of the formulas.For instance, on Wilmott page 787, one may read that '...gamma is related to the amount of rehedging that is expected to take place at the next rehedge and hence to the expected transaction costs...'. I do not quite understand why gamma plays such a role.Also, on page 788, concering Leland model call and put volatilities, one may read that '...a long position in a single call or put with costs incorporated has an apparent volatility that is less than the actual volatility. When the asset price raises the owner of the option must sell some assets to remain delta hedged. But then the effect of the bid-offer spread on the underlying is to reduce the price at which the asset is sold. The effective increase in the asset price is therefore less than the actual increase, being seen as reduced volatility.'.I do not quite understand why the effect of the bid-offer spread on the underlying is to reduce the price at which the asset is sold (is it because excess of supply?).I wonder if anybody could please help.Thank you,

Gamma is the derivative of delta with respect to the stock price, so the higher gamma is the larger the change in delta is for a given change in the stock price, and thus the larger the expected re-hedging amount is. The main point of Leland's argument (which is really just formalized common sense) is that when you act as a delta hedger you are crossing the bid-offer spread each time you re-hedge, which will cost you something. The larger the bid-offer spread, and/or the larger your gamma, the more it will cost you. A nagging problem with this line of analysis is that in the continuous time (Black-Scholes like) limit you will transact enough to incur infinite transaction costs as long as the bid-offer spread is finite, which cannot possibly be a rational (or even possible) thing to do. Flesaker and Hughston (1994, unpublished and hard to find) generalized the Leland result to a continuous time and state economy, but at the cost of assuming infinitesimal transaction costs.

OK, thank you for your reply.Do you know if there are more well-known models allowing for transaction costs, apart from Leland and Flesaker/Hughston ?

QuoteOriginally posted by: bearish... but at the cost of assuming infinitesimal transaction costs.Makes sense. I am sure that if I went to my friendly dealer and said that I was planning on doing infinite trades, they would give me quite a tight bid/offer spread (although not zero!).