vxo: Calculates the old CBOE VIX also known as VXO

In ifrogs: Finance routines developed by the IGIDR Finance Research Group.

Description

This function calculates the volatility index proposed by Whaley (1993) and introduced by the Chicago Board of Exchange known as the old CBOE VIX.

Usage

 vxo(maturity, riskfree, carry, type, strike, underlying, bid=NULL, ask=NULL,
    value=NULL)

Arguments

maturity	A numeric vector specifying time to expiration in years corresponding to each element in ‘type’.
riskfree	A numeric value of the annualized risk-free interest rate to expiration; e.g. 0.16 means 16% pa corresponding to each element in ‘type’.
carry	A numeric value of the annualized cost-of-carry rate; e.g. 0.10 means 10% pa corresponding to each element in ‘type’.
type	A character vector specifying the option type ‘“c”’ and ‘“p”’ for call and put options respectively.
strike	A numeric vector with excercise prices corresponding to each element in ‘type’.
underlying	A numeric vector of the asset prices corresponding to each element in ‘type’.
bid	A numeric vector of best buy prices corresponding to each element in ‘type’.
ask	A numeric vector of best sell prices corresponding to each element in ‘type’.
value	An optional numeric vector of option prices corresponding to each element in ‘type’ when bid and ask prices are not available. If ‘bid’ and ‘ask’ prices are provided then ‘value’ is computed as ‘(bid + ask) / 2’ and any provided ‘value’ is ignored.

Details

The function calculates the old CBOE volatility index. The computation requires eight at-the-money options for two nearest maturities. Therefore each input to the function is a vector of length eigth with elements at each index value corresponding to that option.

The eight options are selected in the following fashion: there should be a pair of call and put options for two unique strikes, one directly above and the other directly below the underlying value. The near month maturity must have at least eight days to maturity.

The implied volatilities are computed for each option by using an option pricing model. Note, that setting ‘carry = riskfree’ we get Black and Scholes' stock option model, ‘carry = riskfree-div’ we get Merton's stock option model with continuous dividend yield ‘div’, ‘carry = 0’ we get Black's futures option model, and ‘carry = riskfree-riskfreef’ we get Garman and Kohlhagen's currency option model with foreign interest rate ‘riskfreef’ (using GBSVolatility from package ‘fOptions’). In addtion, for the Black's Model on futures the ‘underlying’ value specified should be the futures price.

For further details on the computation procedure please see Whaley (1993).

Value

Returns VXO value: a numeric scalar.

Author(s)

Akhil S. Behl [e-mail];
Rohini Grover [e-mail]

References

Whaley, R.E. (1993). “Derivatives on market volatility: hedging tools long over due”, Journal of Derivatives 1, 71-84.

Examples

  # Example 1: SPX options to compute VXO

  data(vxo_spx)

  vxo(maturity=vxo_spx$maturity, riskfree=vxo_spx$riskfree,
     carry=vxo_spx$riskfree, type=vxo_spx$type, strike=vxo_spx$strike,
     underlying=vxo_spx$underlying, bid=vxo_spx$bid, ask=vxo_spx$ask)

  # Example 2: NIFTY options to compute VXO
  data(vxo_nifty)

   vxo(maturity=vxo_nifty$maturity, riskfree=vxo_nifty$riskfree,
      carry=vxo_nifty$riskfree, type=vxo_nifty$type, strike=vxo_nifty$strike,
      underlying=vxo_nifty$underlying, bid=vxo_nifty$bid, ask=vxo_nifty$ask)

ifrogs documentation built on May 31, 2017, 2:27 a.m.