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Consider a European put option, whose price at time $0$ is $\Pi_0$. Set: $$\mathcal{L}_0=\Pi_0 - P(0,t_M)\Pi_{t_M}$$ where 0 < $t_M$ and $P(0, t_M)$ is the discount factor from time $0$ to time $t_M$. Is that correct to state that $\mathcal{L}_0$ represents the present value of a short position on the put option? That is, at time $0$ you have a positive value equal to $\Pi_0$ and at time $t_M$ you will have to rebuy the put option at its current price (i.e. $\Pi_{t_M}$), which enters negatively (and discounted, since you have to evaluate everything at time 0) in the value of your position.

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Close to that. Your formula represents the profit (or loss) of that position as seen from $t_0$, which is so far a stochastic term observable at expiry.

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  • $\begingroup$ With 'that position' you mean a short position on the option, right? $\endgroup$ – Strictly_increasing Mar 30 at 20:37
  • $\begingroup$ Sorry. Yes, of course $\endgroup$ – Kermittfrog Mar 30 at 20:54
  • $\begingroup$ Thank you a lot $\endgroup$ – Strictly_increasing Mar 30 at 21:50

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