Black Scholes Merton and LTCM – Part 1

I have just watched BBC’s documentry about Black-Scholes (for the 10th time).

Black Scholes (BBC)

Every time I watch it i learn something new, mainly because each time my knowledge of the subject matter has significantly increased in between viewings.

The formula below is the fundamental BS equation (solution a la Merton)

C(S,t)=N(d_{1})~S-N(d_{2})~K e^{-r(T-t)}\,

My sister was asking me so why did they assume that the strategies the employed at LTCM will consistently return profits … I’m seriously pondering this. So far I believe that in the long run there startegies failed for several reasons but before we mention them it’s worth saying what these starts were. From general material like Wikipedia, one can deduce most pf the starts were based on mean reverting models (this is essentially the foundation for a pairs trading strategy which LTCM employed extensively.)

Reasons for the demise of LTCM:

  • Assumed non stochastic rates
  • Assumed constant volatility
  • Failure of rationality
  • Fundamental breakdown about the understanding of a pairs trading model.

In part 2 I would delve deeper into the fundamentals.


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