# Level II Derivatives

## Binomial Pricing Trees (for Options)

Binomial trees are used in a variety of contexts in finance: Calculating probabilities for Bayes’ Formula type problems Calculating the value of options on stocks, commodities, and so on (you are here) Calculating the option-adjusted spread (OAS) for bonds Calculating the value of bonds with embedded options Calculating the value of floating-rate bonds Calculating the […]

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## Valuing Equity Swaps

Equity swaps are just as easy to value as plain vanilla interest rate swaps; once again, as with all derivatives, the formula for the value is: $Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)$ If one leg is a fixed or floating rate, it is valued exactly as described for plain vanilla […]

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## Pricing Equity Swaps

Remember that the price of a swap is the fixed rate on the swap.  An equity swap can take many forms: The equity side can pay the return on a single stock, on a portfolio of stocks, or on an equity index. The equity side can pay only the price appreciation on the stock, portfolio, […]

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## Valuing Currency Swaps

Currency swaps are only slightly more difficult to value than plain vanilla interest rate swaps; once again, as with all derivatives, the formula for the value is: $Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)$ Because the swap is equivalent to two bonds (one long, one short, one in one currency, one […]

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## Pricing Currency Swaps

Remember that the price of a swap is the fixed rate on the swap.  A currency swap can take one of three forms: Each side pays a fixed rate: one in one currency, the other in a different currency.  In this case, there are two prices for the currency swap: the two fixed rates (which […]

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## Valuing Plain Vanilla Interest Rate Swaps

Somewhat surprisingly, a plain vanilla interest rate swap is one of the easiest derivatives to value; once again, as with all derivatives, the formula for the value is: $Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)$ Because the swap is equivalent to two bonds (one long, one short, one fixed, one floating), […]

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## Valuing Currency Forwards

The formula for computing the value to the long position of a currency forward is: $V_t\ =\ \frac{S_t}{\left(1\ +\ r_{BC}\right)^{(T\ -\ t)}}\ -\ \frac{F_T}{\left(1\ +\ r_{PC}\right)^{(T\ -\ t)}}$ where: $V_t$: value of the currency forward (to the PC payer / BC receiver) at time $t$ (in $\dfrac{PC}{BC}$) $T$: expiration of the forward contract $S_t$: spot […]

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## Pricing Currency Forwards

A currency forward contract is an agreement to exchange a given amount of one currency for a given amount of another currency at a future date.  The price of a currency forward is the exchange rate for the currencies at the expiration of the contract, and is related to the spot exchange rate by covered […]

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## Valuing FRAs

Recall that an FRA is essentially an agreement to enter into two loans (one long, one short) in the future: a fixed-rate loan and a floating-rate loan.  (The difference between an FRA and an actual agreement to enter into these two loans is that the FRA will be settled at the beginning of the loan […]

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## Valuing Forwards and Futures

The formulae for valuing all derivatives are essentially the same: $Value\ =\ PV(what\ you\ will\ receive)\ –\ PV(what\ you\ will\ pay)$ First, the notation: $V_t$: value of the forward (to the long) at time $t$ $T$: expiration of the forward contract $S_t$: spot price at time $t$ $F_T$: forward price at time $T$ $r_f$: effective […]