optstocksensbylr - Determine option prices and sensitivities using Leisen-Reimer binomial tree model

Syntax

Description

PriceSens = optstocksensbylr(LRTree, OptSpec, Strike, Settle, ExerciseDates) calculates option prices and sensitivities using a Leisen-Reimer binomial tree model.

PriceSens = optstocksensbylr(LRTree, OptSpec, Strike, Settle, ExerciseDates, Name,Value) constructs a Leisen-Reimer stock tree with additional options specified by one or more Name,Value pair arguments.

Input Arguments

LRTree	Stock tree structure created by lrtree.
OptSpec	NINST-by-1 cell array of strings 'call' or 'put'.
Strike	NINST-by-1 (European/American) or NINST-by-NSTRIKES (Bermuda) matrix of strike price values. Each row is the schedule for one option. If an option has fewer than NSTRIKES exercise opportunities, the end of the row is padded with NaNs.
Settle	NINST-by-1 matrix of settlement or trade dates.
ExerciseDates	NINST-by-1(European/American) or NINST-by-NSTRIKEDATES (Bermuda) matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only one ExerciseDate on the option expiry date. For the American type, the option can be exercised on any tree data between the ValuationDate and tree maturity. The last element of each row must be the same as the maturity of the tree.

Name-Value Pair Arguments

'AmericanOpt'	NINST-by-1 flags with values of 0 (European/Bermuda) or 1 (American). Default: 0
'OutSpec'	NOUT-by-1 or 1-by-NOUT cell array of strings indicating the nature and order of the outputs for the function. Possible values are Price, Delta, Gamma, Vega, Lambda, Rho, and All. Default: Price

Output Arguments

PriceSens

NINST-by-1 expected prices or sensitivities values.

Examples

Consider European call and put options with an exercise price of $100 that expire on December 1, 2010. The underlying stock is trading at $100 on June 1, 2010 and has a volatility of 30% per annum. The annualized continuously compounded risk-free rate is 7% per annum. Using this data, compute the price, delta and gamma of the options using the Leisen-Reimer model with a tree of 25 time steps and the PP2 method.

AssetPrice  = 100;
Strike = 100;

ValuationDate = 'June-1-2010';
Maturity = 'December-1-2010'; 

%Define StockSpec
Sigma = 0.3;

StockSpec = stockspec(Sigma, AssetPrice);

% Define RateSpec
Rates = 0.07;
Settle = ValuationDate;
Basis = 1;
Compounding = -1;

RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', Settle, ...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis);

%Build the Leisen-Reimer (LR) tree with 25 time steps
LRTimeSpec  = lrtimespec(ValuationDate, Maturity, 25); 

% Use the PP2 method
LRMethod  = 'PP2';  

TreeLR = lrtree(StockSpec, RateSpec, LRTimeSpec, Strike, 'method', LRMethod);

%Compute prices and sensitivities using the LR model:
OptSpec = {'call'; 'put'}; 
OutSpec = {'Price', 'Delta', 'Gamma'};

[Price, Delta, Gamma] = optstocksensbylr(TreeLR, OptSpec, Strike, Settle, ... 
Maturity, 'OutSpec', OutSpec)

Price =

   10.1332
    6.6937

Delta =

    0.6056
   -0.3944

Gamma =

    0.0185
    0.0185

References

Leisen D.P., M. Reimer, "Binomial Models for Option Valuation – Examining and Improving Convergence," Applied Mathematical Finance, Number 3, 1996, pp. 319-346.

See Also

lrtree | optstockbylr

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