Implied Volatility is the volatility derived from an option with a known price (or premium). If the price of an option is known, the other inputs (such as spot, strike, time etc) can be either taken from the option contract or market data sources, thus the only remaining unknown input – the volatility can be solved for. The Black Scholes option pricing formula cannot be reversed to express volatility in terms of other inputs so an iterative approach is required by testing different volatilities.
Historic Volatility Calculator
Historic Volatility is the volatility of an asset based on its past price movements. The volatility of the underlying asset for the option’s remaining life is a key input into most option pricing models, however this volatility is never in practice observable since it is based on future price movements which cannot be known. Thus, volatility must be forecast, and one method of forecast is to use the historic volatility of the asset which is calculated from its past price movements.
CFA Community Launches
CFA Analyst Republic is a community and resources sites for candidates taking the CFA exam. Since much of our derivatives experience was relevant to the Quantitative Methods part of the CFA Syllabus we contributed some the derivatives and statistical notes (such as the measures of mean ).
In addition there is a CFA Forum for asking for help with CFA material.
Black Scholes Inputs
The Black Scholes model has five main inputs:
Spot Price :
The market price of the underlying asset on the valuation date. This can be a difficult input to estimate for options on illiquid assets, however under normal circumstances the closing market price can usually be used
Interest Rate Swap Example
An Interest Rate Swap is the exchange of a stream of cash flows based on a fixed interest rate in exchange for a stream of cash flows based on a floating interest rate.
For example, Party A is currently paying a floating rate of interest but wishes to convert that to a fixed rate of interest. Party B is currently paying a fixed rate of interest but wishes to pay a floating rate. The two parties can enter into an interest rate swap whereby Party A pays a fixed rate to B in exchange for a floating rate of interest. The net result (as shown in the example below) is that Party A ends up paying a floating rate of interest and Party B ends up with a fixed rate of interest.
FAS 133 / IAS 39 Hedge Effectiveness
>Hedge effectiveness is the test applied to a hedging instrument to ascertain whether it will be eligible for hedge accounting. Hedge accounting allows a heding instrument (normally a derivative) to be exempt fromt he mark-to-market requirement of FAS 133 and IAS 39, instead the instrument is carried on the balance at its fairmarket value but the gains and losses are instead posted to reserves and not to the Income Statement.
There are two types of hedge – cash flow hedge and fair value hedge. A cash flow hedge matches cash flows from an instrument with predictable cash flows from a hedging instrument. A fair value hedge matches the changes in fair value in the underlying insturmnet with the cahnges in fair value of the hedging instrument.
FAS 133 Derivatives Valuation Tools
Financial Advisory Standard (FAS) 133 was introduced to enhance the relevancy of accounts for derivatives and other offbalance sheet items which had previously not been included int he accounting standards. FAS 133 is the equivalent of IFRS 39, but differs from FRS 13 in that FRS 13 is for disclosure purposes only and does not include any on PL account accounting for derivatives transactions. Under FAS 133 all derivatives must be valued at the market value with the change in valuation flowing through the PL account, it is possible to have the value hedge accounted however.
Cross Currency Swap Valuation
A cross currency swap is swap of an interest rate in one currency for an interest rate payment in another currency. For example, a cross currency swap could be an exchange of a fixed stream of cash flows in US Dollars for a floating rate stream of cash flows in Euros. This could be considered an interest rate swap with a currency component.
Currency Swaps are typically valued using a standard discounting procedure whereby each stream of cash flows is discounted using the yield curve of that currency and finally the NPV of each leg is then converted at the spot exchange rate.