naginterfaces.library.specfun.opt_​lookback_​fls_​price

naginterfaces.library.specfun.opt_lookback_fls_price(calput, sm, s, t, sigma, r, q)[source]

opt_lookback_fls_price computes the price of a floating-strike lookback option.

For full information please refer to the NAG Library document for s30ba

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s30baf.html

Parameters
calputstr, length 1

Determines whether the option is a call or a put.

A call; the holder has a right to buy.

A put; the holder has a right to sell.

smfloat, array-like, shape

must contain , the th minimum observed price of the underlying asset when , or , the maximum observed price when , for .

sfloat

, the price of the underlying asset.

tfloat, array-like, shape

must contain , the th time, in years, to expiry, for .

sigmafloat

, the volatility of the underlying asset. Note that a rate of 15% should be entered as .

rfloat

, the annual risk-free interest rate, continuously compounded. Note that a rate of 5% should be entered as .

qfloat

, the annual continuous yield rate. Note that a rate of 8% should be entered as .

Returns
pfloat, ndarray, shape

contains , the option price evaluated for the minimum or maximum observed price or at expiry for and .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry with a put option, .

Constraint: for put options, for all .

(errno )

On entry with a call option, .

Constraint: for call options, for all .

(errno )

On entry, .

Constraint: for all .

(errno )

On entry, .

Constraint: and .

(errno )

On entry, .

Constraint: for all .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

opt_lookback_fls_price computes the price of a floating-strike lookback call or put option. A call option of this type confers the right to buy the underlying asset at the lowest price, , observed during the lifetime of the contract. A put option gives the holder the right to sell the underlying asset at the maximum price, , observed during the lifetime of the contract. Thus, at expiry, the payoff for a call option is , and for a put, .

For a given minimum value the price of a floating-strike lookback call with underlying asset price, , and time to expiry, , is

where . The volatility, , risk-free interest rate, , and annualised dividend yield, , are constants. When , the option price is given by

The corresponding put price is (for ),

When ,

In the above, denotes the cumulative Normal distribution function,

where denotes the standard Normal probability density function

and

where is taken to be the minimum price attained by the underlying asset, , for a call and the maximum price, , for a put.

The option price is computed for each minimum or maximum observed price in a set or , , and for each expiry time in a set , .

References

Goldman, B M, Sosin, H B and Gatto, M A, 1979, Path dependent options: buy at the low, sell at the high, Journal of Finance (34), 1111–1127