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a binary option that is out of money right now but has an unlimited time to expiry? What would be a good approach to price this?

QuoteOriginally posted by: mrmea binary option that is out of money right now but has an unlimited time to expiry? What would be a good approach to price this?100

QuoteOriginally posted by: PaperCutQuoteOriginally posted by: mrmea binary option that is out of money right now but has an unlimited time to expiry? What would be a good approach to price this?100indeed, or just drop the time term from Black-Scholes, see perpetual options in professa' wilmott's ooksI take it this is either American or a barrier ?

Could you be more explicit...I have this option, the spot is 60 now, and I will be paid 100 if the underlying hits 100. Else I can wait till infinity.What is the price of this option? is this an perpetual american digital opt?I can assume GBM, and either suggest an analytical solution or get numerical with simulation, finite differences or binomial tree.Thanks for your help. help is urgent.

Could you be more explicit...I have this option, the spot is 60 now, and I will be paid 100 if the underlying hits 100. Else I can wait till infinity.What is the price of this option? is this an perpetual american digital opt?And I have found this.http://www.elitetrader.com/vb/printthre ... did=25616I can assume GBM, and either suggest an analytical solution or get numerical with simulation, finite differences or binomial tree.Thanks for your help. help is urgent.

QuoteOriginally posted by: mrmeI have this option, the spot is 60 now, and I will be paid 100 if the underlying hits 100. Else I can wait till infinity.it's a perpetual barrier option

This following topic answers my question for r=0.http://www.wilmottmagazine.com/messagev ... E=1However for r=a constant nonzero rate, what would be the answer. Would 1/H would still be a hedge?

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QuoteOriginally posted by: mrmethe spot is 60 now, and I will be paid 100 if the underlying hits 100. Else I can wait till infinity..if the interest rate is constant and non-zero, the price of the option is the current price of the stock:in your case, 60.Consider the following option with a finite life T:payoff=100 if underlying hits 100 for t<Tpayoff at time T=stock price S if S<100 You can hedge this perfectly by holding the stock, so value of the finite-life option is S (stock price) independent of T.Now let T -> infinity, and you have the perpetual option

QuoteOriginally posted by: ppauperif the interest rate is constant and non-zero, the price of the option is the current price of the stock:in your case, 60.[static hedge explained]That won't work with non-zero interest rates because it gives only a 1-way hedge - only an upper bound. If you hedged a bought option that way you would still have to carry the short stock position that financed your option purchase.Douady's 2000 paper "Closed Form Formulas for Exotic Options and their Lifetime Distribution" does what it says on the tin, and this is one of the problems he solves. He himself, however, cautions against indiscrimminate use of these formulas which assume constant interest rates and volatility.As a practical matter, if you can already price an ordinary 1-touch digital of finite expiry, you will probably find that the price converges as you extend the expiry.

QuoteOriginally posted by: PKKoopThat won't work with non-zero interest rates because it gives only a 1-way hedge - only an upper bound. If you hedged a bought option that way you would still have to carry the short stock position that financed your option purchase.If you set it up the way I did, with an expiration at time T, a payoff on the barrier for t<T and a payoff of S at time T if the barrier is not hit,then the value of that payoff at time T tends to zero as T -> infinity provided the interest rate is positive.