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There are "perpetual" bonds and preferred shares that are traded in the corporate credit markets that exactly match your conditions above. They are recorded in the 10-K at notional value $X$. The "close-out" feature is an embedded call. You should assume your favorite stochastic interest rate (and/or credit) model and run a PDE solver, tree, or other grid ...


As with most derivatives that have early exercise, you are going to want to price this using a grid scheme. I have priced callable loans with floors using the Generalized Vasicek model at my old hedge fund, and it is fairly easy to handle. As a matter of fact my students are doing that very problem as homework this week, and my reference implementation ...


The answer to your first four questions is affirmative. Option-adjusting the spread makes an equivalence between everything theoretically possible, but the quality of results depends significantly on the quality of your interest rate model and its calibration. My personal opinion, though, is that the results need to be treated carefully because the OAS ...


honestly your question is hard to understand. Are these two questions the same? "Does fitting sub-optimal option exercise strategies to market data yield better option values?" "which modeling approach leads to better predictions and better relative value measures?" I think you want to ask 1 and I think it is similar to Setting the r in put-call parity? ...


You have to look at the terms and conditions on your individual bond. The way the specifications usually work is that a call will result in accrued interest being paid, effectively making up for the lost coupon. Sometimes there's even an extra penalty. A put will result in a loss of coupon in almost all cases, and so is almost always done just after a ...


Use the USD rate. The actual tricky bit is in the volatility. Normally for a cross currency bond you would use the volatility of the foreign shares as denominated in US currency. However, the fixed FX rate in this case means that the correct volatility to use is the volatility in INR.


The answer is, that it does not matter. Choose one currency as the numeraire, and stick to it. This is because of the foreign exchange interest rate carry arbitrage relationship. If that relationship doesn't hold, skip the bond and lock-in the arbitrage on the interest rate differential embedded in the USD/INR exchange rate.

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