Thanks for the great lecture! One question: at 11:35 isn't it trivial to get C(0) = 0.764? because you derived probability q in a such way of discounting with risk-free rate and with same u and d, so you must get the same C(0). Or am I missing something?
Because risk-adapted discount rate and real world probabilities are notoriously difficult to estimate, in some sense they are by definition unobservable, or at the very least subjective. If we instead adopt the risk neutral pricing paradigm, all we need to know is the information of the current market, one single snapshot at time t (for simple claims), and that's it. Not to mention the plethora of mathematical tools that deal with pde, martingale, stochastic caculus etc, the whole problem of option pricing suddenly becomes manageable. This is why Scholes and Merton got the Nobel prize.
@@Boringpenguin but even if everyone could compute real-world probabilities, wouldnt that still imply market equilibrium? The risk neutral measure would still apply.
Thanks for the great lecture! One question: at 11:35 isn't it trivial to get C(0) = 0.764? because you derived probability q in a such way of discounting with risk-free rate and with same u and d, so you must get the same C(0). Or am I missing something?
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Why bother with RN probabilities if we could instead use a risk-adapted discount rate together with the real world probs?
Because risk-adapted discount rate and real world probabilities are notoriously difficult to estimate, in some sense they are by definition unobservable, or at the very least subjective. If we instead adopt the risk neutral pricing paradigm, all we need to know is the information of the current market, one single snapshot at time t (for simple claims), and that's it. Not to mention the plethora of mathematical tools that deal with pde, martingale, stochastic caculus etc, the whole problem of option pricing suddenly becomes manageable. This is why Scholes and Merton got the Nobel prize.
@@Boringpenguin but even if everyone could compute real-world probabilities, wouldnt that still imply market equilibrium? The risk neutral measure would still apply.