vix_ci: Computes confidence interval for model-based volatility...

In igidrfrg/ifrogs: Finance Routines Developed by the Finance Research Group

Description

This function implements the methodology for constructing confidence intervals for model based volatility indexes as described in Grover and Shah (2013). The four model based indexes provided are described in Grover and Thomas (2012).

Usage

vix_ci(prep_near, prep_next, n_samples=1e3, conf=0.95, verbose=TRUE, ...)

Arguments

prep_near	A list of objects returned by ‘prep_maturity’ for the near month maturity.
prep_next	A list of objects returned by ‘prep_maturity’ for the next month maturity. If not available it is set as ‘NULL’.
n_samples	A positive integer of the number of bootstrap replicates.
conf	A scalar containing the confidence level of the required interval.
verbose	A logical value indicating whether warning messages from ‘boot’ be printed.
...	Further arguments to be passed to ‘boot’.

Details

The function consumes as ‘prep_near’ and ‘prep_next’ the output returned by ‘prep_maturity’ for each maturity.

If options are not available for the next maturity, prep_next=NULL may be used to compute the confidence interval for weighted average IV for only the near maturity. In this case the weighted average implied volatility is converted to a percentage.

The adjusted bootstrap percentile method of Efron (1987) is used to compute the confidence interval.

Value

Returns a list of following three elements.

point	A numeric value/vector of the point estimates of VIXes.
ci	The lower and upper confidence limits corresponding to each volatility index computed.
samples	The bootstrap replicates of the volatility index/indexes computed.

Author(s)

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

References

Grover, R. and Thomas, S. (2012). “Liquidity Considerations in Estimating Implied Volatility”, Journal of Futures Market, 32, 714 - 741.

Grover, R. and Shah, A. (2013). “The imprecision of volatility indexes”.

See Also

boot.ci, prep_maturity, weighted_iv

Examples

  # Example 1: Construct confidence interval for Vega VIX using SPX options

  set.seed(101)
  data(vix_spx)

  # Preparing data for near and next month spx options without filtering
  # options with zero traded volume.
  spx_near <- prep_maturity(maturity=vix_spx$opt_near$maturity[[1]],
                            riskfree=vix_spx$opt_near$riskfree[[1]],
                            carry=vix_spx$opt_near$riskfree[[1]],
                            type=vix_spx$opt_near$type,
                            strike=vix_spx$opt_near$strike,
                            underlying=vix_spx$opt_near$underlying,
                            schemes="vega",
                            bid=vix_spx$opt_near$bid,
                            ask=vix_spx$opt_near$ask,
                            tv_filter=FALSE)

  spx_next <- prep_maturity(maturity=vix_spx$opt_next$maturity[[1]],
                            riskfree=vix_spx$opt_next$riskfree[[1]],
                            carry=vix_spx$opt_next$riskfree[[1]],
                            type=vix_spx$opt_next$type,
                            strike=vix_spx$opt_next$strike,
                            underlying=vix_spx$opt_next$underlying,
                            schemes="vega",
                            bid=vix_spx$opt_next$bid,
                            ask=vix_spx$opt_next$ask,
                            tv_filter=FALSE)

  # Confidence interval for Vega VIX
  spx_ci <- vix_ci(prep_near=spx_near,
                   prep_next=spx_next,
                   n_samples=1e3, conf=0.95,
                   verbose=TRUE)

  str(spx_ci)

  # Point estimate
  spx_ci$point

  # Confidence interval
  spx_ci$ci

  # Bootstrap replicates
  head(spx_ci$samples)

  # Example 2: Compute Vega VIX using NIFTY options
  set.seed(101)
  data(vix_nifty)

  # Preparing data for near and next month nifty options and filtering options
  # with zero traded volume.
  nifty_near <- prep_maturity(maturity=vix_nifty$opt_near$maturity[[1]],
                              riskfree=vix_nifty$opt_near$riskfree[[1]],
                              carry=vix_nifty$opt_near$riskfree[[1]],
                              type=vix_nifty$opt_near$type,
                              strike=vix_nifty$opt_near$strike,
                              underlying=vix_nifty$opt_near$underlying,
                              schemes="vega",
                              bid=vix_nifty$opt_near$bid,
                              ask=vix_nifty$opt_near$ask,
                              traded_vol=vix_nifty$opt_near$traded_vol,
                              tv_filter=TRUE)

  nifty_next <- prep_maturity(maturity=vix_nifty$opt_next$maturity[[1]],
                              riskfree=vix_nifty$opt_next$riskfree[[1]],
                              carry=vix_nifty$opt_next$riskfree[[1]],
                              type=vix_nifty$opt_next$type,
                              strike=vix_nifty$opt_next$strike,
                              underlying=vix_nifty$opt_next$underlying,
                              schemes="vega",
                              bid=vix_nifty$opt_next$bid,
                              ask=vix_nifty$opt_next$ask,
                              traded_vol=vix_nifty$opt_next$traded_vol,
                              tv_filter=TRUE)
  # Confidence interval for Vega VIX
  nifty_ci <- vix_ci(prep_near=nifty_near,
                    prep_next=nifty_next,
                    n_samples=1e3, conf=0.95,
                    verbose=TRUE)

  str(nifty_ci)

  # Point estimate
  nifty_ci$point

  # Confidence interval
  nifty_ci$ci

  # Bootstrap replicates
  head(nifty_ci$samples)

igidrfrg/ifrogs documentation built on July 20, 2020, 2:02 p.m.