Arbitrary Cash-Flow Model

An Arbitrary Cash-Flow (ACF) security interface values future known cash-flows. These cash-flows must be in a single (potentially foreign) currency.

Pricing Arbitrary Cash-Flow

An Arbitrary Cash-Flow (ACF) security interface values future known cash-flows. These cash-flows must be in a single (potentially foreign) currency. The present value of these cash-flows is determined by prevailing market interest and foreign exchange rates.

Suppose denote known future cash-flows, which occur at the known times If denotes the risk-free discount factor to time T for the cash-flow currency, then GET applies the following valuation formula to obtain the present value (PV) of the above cash-flows

Here, is the spot market foreign exchange (FX) rate from the cash-flow currency into the domestic currency.

If denote Imagine interest rate maturity dates for the simply compounded rates then our benchmark assumed piece-wise constant continuously compounded instantaneous forward rates f(t) given by. In addition, the following is satisfied for all

Moreover, for we have

We note that, in the above, we equivalently apply log-linear interpolation of discount factors.

In the case, when we considered an Imagine bond par yield curve input, we performed the following calculations:

Suppose denoted annually compounded par yields, with respect to maturities for bonds . Thus, bond has an annual coupon equal to

We performed a bootstrap to obtain the discount factors In particular,

we applied the following recursive formulas

The equations above are derived from the following observation; given a notional of 100

the price of the par yield bond is 100. Thus,

Finally, we assume as above that continuously compounded instantaneous forward rates f(t) satisfy

that is, log-linear interpolation of discount factors.

The implementation requires the following input parameters:

· Future cash-flow amounts,

· Future cash-flow times,

· Cash-flow currency,

· Domestic currency,

· Spot FX rate from the cash-flow to the domestic currency,

· Imagine interest rate curve for the cash-flow currency.

For a rate curve, the user must specify the following:

· a series of interest rates with start and end dates,

· interest rate compounding,

· day count convention.

For a bond yield curve (ref https://finpricing.com/lib/IrCurveIntroduction.html), the user must specify the following:

· a series of bond yields with maturity dates,

· bond yield compounding,

· day count convention,

· coupon frequency,

· coupon amounts (as percentage of notional amount).

For a discount curve, the user must specify a series of discount factors and discount dates.

We test the model with respect to the following representative interest rate curve inputs:

· Flat continuously compounded interest rate curve,

· Simply compounded spot yield curve,

· Discount factor curve,

· Annual coupon par yield curve.