Can anyone give a formulation on how to express that a self financing hedging strategy is a martingale?I'm working with delta-hedging short european call options. I understand some of the parts of the argument but still i cannot link it together so to argue fluently.The girsanov theorem might be essential: we transform the measure P to Q which is a risk neutral world. - I've read somewhere that both the diffusion and the drift term cancel out, then what is left? ... or in another way we have that: and inserting it in we get that :the girsanov kernel ~ market price of risk. ---But what have we really done here? ... by saying that, does it mean that the self-financing hedging strategy is a martingale? ...Shortly, i'm confused about the link between martingale, risk neutrality and arbitrage free. In my head i have: martingale->risk neutral->arbitrage free. Bad image?Thanks in advance.

A martingale is a process with drift zero--the epectation of its value in the future is equal to the present value.Risk-neutral means the market price of risk is zero. For this to happen, the drift must be equal to the risk-free rate.Arbitrage free just means there cannot be risk-free profits greater than the risk-free rate. If two portfolios have the same payout in all states in the future, they must have the same price today.

QuoteOriginally posted by: bwarrenA martingale is a process with drift zero--the epectation of its value in the future is equal to the present value.Risk-neutral means the market price of risk is zero. For this to happen, the drift must be equal to the risk-free rate.Arbitrage free just means there cannot be risk-free profits greater than the risk-free rate. If two portfolios have the same payout in all states in the future, they must have the same price today.Thanks for the decomposition. so when we have risk-neutrality we might say that the process is a martingale because the market price of risk is 0 i.e. the drift=0 -> martingale.

But the drift is not zero, it is r. It is not a martingale.

QuoteOriginally posted by: cedicon the self-financing hedging strategy is a martingale? ...I'd say "the discounted value of a self-financing portfolio is a martingale under the risk-neutral probability." The change to the Risk-neutral measure makes the drift equal to r. Discounting (play around with Ito's lemma) makes this drift equal to r - r = 0.