How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

Like the formula on page 282 of your big book when [$]n[$] is prime?

How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

Like the formula on page 282 of your big book when [$]n[$] is prime?

yes that is possibly a way to go I think. And lets add a barrier H, after barrier hit it switch to pay $1 on every Fibonacci prime.

Useful hedging instrument for Fibo traders?

How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

For any (continuously monitored) diffusion, I'd say the option is worth [$]+\infty[$], as there is a positive probability of reaching S - X = 3, for example, and once attained, that level will be crossed an infinite number of times during the lifetime of the option.

How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

For any (continuously monitored) diffusion, I'd say the option is worth [$]+\infty[$], as there is a positive probability of reaching S - X = 3, for example, and once attained, that level will be crossed an infinite number of times during the lifetime of the option.

okay so we need to introduce condition that pay at prime-touch and then has to touch another prime before the previous prime comes back into play again.

Back to the past option: Time to maturity T, time traveler period tau, strike K and barrier H . When S_t hits the barrier H you get paid out max(S_(t-tau)-X,0) for a call. The interesting thing is when you are close to the barrier you are also quite sure on the pay-off, but never sure before you hit the barrier and the option is sent back in time.  So price path in past (liked to pay-off) is naturally known, the time-travel path liked to future is stochastic, you never know what date your option ends up time-traveling, but it will be somewhere between -tau and T-tau for this variant, if not expiring out of time. The time point you travel back to the past is stochastic, a barrier hit probability. In more exotic variants we could make tau stochastic.

If t-tau is on a day time-travel pay-off is OTM then you prefer S_t>>H so you not are sent back to the past and get zero pay-off. When t-tau is a day when S_(t-tau)-K is large u want S_t be close to H and hopefully be sent back in time. If sent back to a bank holiday you also lost the option.

Make some sense to buy such options for people that are strong believers that certain dates etc in past and future are linked. It is not too late to make money on the crash of 87, just choose tau=today - Crash-87 date + T.

Can make many cool variants here, there exist a large class of time-travel derivatives. 

Typical buyer: fans of Back to The Future, The Time Macine and The Time Traveler's Wife (a Chicago librarian with a paranormal genetic disorder that causes him to randomly time travel).
Typical naked short sellers, people not believing in time-traveling. 
Typical market maker: time travel arbitrageur.
Compliance: Timecop.
There is clearly a market here, not large, but a nice niche product. 

Also a large market to back-traders. Many of them. Second chance options! 

Alan I am sure can come up with a formula for that, possibly even including discrete dividend.  

Good one. Yeah, I think I can value it for a diffusion. 

Suppose you want to value it at time [$]t[$] prior to expiration [$]T[$]. The state variable, which you must be given, is the S-path history from [$]t-\tau[$] to [$]t[$]. Then, the option value V(t) breaks up into two pieces [$]V_1(t) + V_2(t)[$]. You can think of [$]t[$] as an arbitrary fixed time in the interval [$](0,T)[$].

I assume [$]T-\tau > t[$] or otherwise [$]V_1(t)[$] below is the only contribution. In other words, as time runs toward expiration, there are two pieces to the value formula until you reach the times [$]t[$] close to expiration where [$]T - t < \tau[$]. At those "close" times, only the [$]V_1(t)[$] formula below applies. 

[$]V_1(t)[$] is the value conditional on a barrier hit at time [$]s \in (t,t+\tau)[$]. For those hits, given s, the payoff involves [$]S(s-\tau)[$] which is known at time t because it is part of the state. Let [$]p_{hit}(s)[$] be the hitting time density for the first hit on H occurring at time [$]s[$], where [$]s>t[$], and suppressing the dependence upon [$](t,S(t),H)[$]. Then

(*) [$]V_1(t) = \int_t^{t+\tau} \max [S(s - \tau) - X, 0] \, p_{hit}(s) \, ds[$]   

There are routine formulas for [$]p_{hit}(\cdot)[$] for GBM, but you can find it numerically for any diffusion.

The next part [$]V_2(t)[$] is slightly trickier. [$]V_2(t)[$] is the value conditional on a barrier hit at time [$]s \in (t+\tau,T)[$].  For those hits, given s, the payoff involves [$]S(s-\tau)[$] which is unknown at time [$]t[$] because it is part of the future at [$]t[$]. Nevertheless, if the hit of H occurs at time s, the probability density for [$]S(s-\tau)[$] is computable at time t because it is a bridge density. 

In other words, you need the probability density of observing [$]S(t_1) = Y[$] for [$]t < t_1 < s[$], conditional on knowing both [$]S(t)[$] and [$]S(s)=H[$],
which you do know. Again this bridge process density is routine for GBM, where it's essentially a Brownian bridge density, but it also can be computed numerically for any diffusion. Let's call it [$]p_{bridge}(Y|t_1, S(t),S(s)=H)[$]. Then

  [$]V_2(t) = \int_{t+\tau}^T \int_{X}^{\infty} (Y - X) \, p_{hit}(s) \, p_{bridge}(Y| s-\tau,S(t),S(s)=H) \, dY \, ds[$]

 Final note. If [$]t[$] is a "close" time, then in (*) the upper limit on the integral is T and, as I mentioned, [$]V_2[$] does not contribute.

Very nice! 

Anything left worth reading?

How do u price an option that pays off $1 every time max(S-X,0) during the life time of the option passes through a prime number? 

Numerical should be easy enough, closed form please, trivial?

Prime time derivatives! Sorry, yes I know boring.

Like the formula on page 282 of your big book when [$]n[$] is prime?

yes that is possibly a way to go I think. And lets add a barrier H, after barrier hit it switch to pay $1 on every Fibonacci prime.

Useful hedging instrument for Fibo traders?

Big problem!
Each Fibonacci number is as bad as the previous two put together, Like dead wood.

I'm bored with Brexit. I'm waiting impatiently until it's over and wish Britain could float away.

I'm bored with Brexit. I'm waiting impatiently until it's over and wish Britain could float away.

worse things can happen to an island

I'm bored with Brexit. I'm waiting impatiently until it's over and wish Britain could float away.

worse things can happen to an island

Just watch out for lighthouses

I'm bored with Brexit. I'm waiting impatiently until it's over and wish Britain could float away.

In which direction? There's not much room for manoeuvre! Unless to Norge.

Irrelevant. The further away the better.

https://vimeo.com/111458975