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3

As long as your market is complete and $\tau$ is measurable w.r.t. the filtration generated by the market the continuous cash flow paid until $\tau$ is a hedgeable contingent claim and you have to work under the risk neutral measure.


2

Pricing always takes place under the risk neutral probability measure. In fact, this would make the price more conservative (i.e. lower) with respect to risk; if you priced it under the true measure you would be putting a smaller hazard rate for this random time. Completeness make the risk neutral probability measure unique. In your case you might have ...


2

We can value equity as a call option on the value of the firm, where exercising the option requires that the firm be liquidated and the face value of the debt (which corresponds to the exercise price) paid off. The parameters of equity as a call option are as follows: Value of the underlying asset = S = Value of the firm = 100 Exercise price/Strike ...


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This is actually no different from pricing a "standard" swap. The par swap rate is the "c" solved from $$ \sum_{i=1}^n c \cdot \delta_i \cdot d(t_i) = \sum_{j=1}^N \Delta_j \cdot (l_j + x) \cdot d(t_j). $$ The left hand side is the present value of the fixed payments, where $n$ is the number of fixed leg payments, $\delta_i$ is the day count fraction for ...


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You can't calculate the term swap rate from that information. The problem is that the swap spread (ie difference between swap rate and government bond yield) has a term structure determined by supply and demand, that cannot be calculated.


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Can you tell me if my understanding is correct? Yes it's correct, with minor clarification: you're valuing "ex dividend", meaning for FY2017, e.g., you're valuing the company the next moment the dividend was paid out. Should you be interested in "cum dividend" value, you'd add the value of dividends for the year you are entitled for. ...then what ...


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If I understood the problem, you are valuying the swap in the 1st year. The MtM, as you know, is the difference of both legs. The value of your swap will be: 100*(1+3.95%)-100*(1+2%)=1.95 in year 1. If you want to calculate the MtM value, just divide by the floating rate: 1.95/(1+2%)=1.911. This is from the fix leg side. If you just change it to the ...


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we should first define some notation before discussing pricing. Let $t_0$ be initial time and $ t_1, . . . , t_M$ be pre-specified exercise dates with $t_0 < t_1 < · · · < t_M = T$ , the final maturity, and $Δt = t_m−t_{m−1}$. Without a loss of generality it is assumed exercise dates are equidistant. To price a Bermudan option, its value is split ...


1

This is pretty much exactly the problem description for a standard over-the-counter FX option pricing tool from 10-20 years ago. (For more modern contexts, the data would almost surely contain also 10 delta RR and BF, and perhaps more points as well.) The best solution is, don't build this yourself, but instead use a prexisting tool. FX conventions are ...



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