The Daiquiri Smile
Posted At : April 14, 2008 8:05 PM | Posted By : Pablo Triana
Related Categories: Black-Scholes
Few people seem to understand that when you fudge the vol parameter in BSM (assuming that you are using BSM to price options) it no longer is BSM. It´s simple: the instructions did not say anything about vol fudging, vol is not supposed to be fudged with, vol is supposed to be independent of strike, if you fudge vol is not the same construct anymore it´s something else.
Let me provide what could be seen as a clarifying analogy (or, perhaps, as a complete waste of time). The Daiquiri cocktail was apparently invented by American engineer Jennings Cox in 1905. What could be deemed Cox´s drink is supposed to contain 4,5 cl of white rum, 2 cl of lime juice, and 0,5 cl of gomme syrup. That´s what Cox had in mind when coming up with the invention. Those were the instructions. Very precise.
Now, imagine that in real life you begin to observe that barmen all over the country are mixing it up differently. Depending on the room temperature, they would fudge the lime juice ingredient so as to obtain a more realistic output. If we plotted temperature and lime juice amounts we would get a smiling shape: the lime juice variable would be assigned higher values by barmen the more extreme the room temperature. That is, implied lime juice would smile at us.
Could we still call such real-world daiquiries Cox´s daiquiri? Of course not. Cox said nothing (I hope!) about fudging the lime juice figure. It was supposed to be constant, unaltered. If we do alter it, the final output can´t be called Cox´s daiquiri. It´s something else (Hemingway´s daiquiri?)
If you are given a toy with very precise instructions and you choose to violate such instructions through shameless manipulation, you are betraying the original spirit of the inventors, so much that it no longer is the invention that those original inventors devised.
