This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

minassetsensbystulz

Determine European rainbow option prices or sensitivities on minimum of two risky assets using Stulz option pricing model

Syntax

PriceSens = minassetsensbystulz(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr)
PriceSens = minassetsensbystulz(___,Name,Value)

Description

example

PriceSens = minassetsensbystulz(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr) computes option prices using the Stulz option pricing model.

example

PriceSens = minassetsensbystulz(___,Name,Value) specifies options using one or more optional name-value pair arguments in addition to the input arguments in the previous syntax.

Examples

collapse all

Consider a European rainbow put option that gives the holder the right to sell either stock A or stock B at a strike of 50.25, whichever has the lower value on the expiration date May 15, 2009. On November 15, 2008, stock A is trading at 49.75 with a continuous annual dividend yield of 4.5% and has a return volatility of 11%. Stock B is trading at 51 with a continuous dividend yield of 5% and has a return volatility of 16%. The risk-free rate is 4.5%. Using this data, if the correlation between the rates of return is -0.5, 0, and 0.5, calculate the price and sensitivity of the minimum of two assets that are European rainbow put options. First, create the RateSpec:

Settle = 'Nov-15-2008';
Maturity = 'May-15-2009';
Rates = 0.045;
Basis = 1;

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', Basis)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9778
            Rates: 0.0450
         EndTimes: 0.5000
       StartTimes: 0
         EndDates: 733908
       StartDates: 733727
    ValuationDate: 733727
            Basis: 1
     EndMonthRule: 1

Create the two StockSpec definitions.

AssetPriceA = 49.75;
AssetPriceB = 51;
SigmaA = 0.11;
SigmaB = 0.16;
DivA = 0.045; 
DivB = 0.05; 

StockSpecA = stockspec(SigmaA, AssetPriceA, 'continuous', DivA)
StockSpecA = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1100
         AssetPrice: 49.7500
       DividendType: {'continuous'}
    DividendAmounts: 0.0450
    ExDividendDates: []

StockSpecB = stockspec(SigmaB, AssetPriceB, 'continuous', DivB)
StockSpecB = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1600
         AssetPrice: 51
       DividendType: {'continuous'}
    DividendAmounts: 0.0500
    ExDividendDates: []

Calculate price and delta for different correlation levels.

Strike = 50.25;
Corr = [-0.5;0;0.5];
OptSpec = 'put';
OutSpec = {'Price'; 'delta'};
[P, D] = minassetsensbystulz(RateSpec, StockSpecA, StockSpecB,...
Settle, Maturity, OptSpec, Strike, Corr, 'OutSpec', OutSpec)
P = 3×1

    3.4320
    3.1384
    2.7694

D = 3×2

   -0.4183   -0.3496
   -0.3746   -0.3189
   -0.3304   -0.2905

The output Delta has two columns: the first column represents the Delta with respect to the stock A (asset 1), and the second column represents the Delta with respect to the stock B (asset 2). The value 0.4183 represents Delta with respect to the stock A for a correlation level of -0.5. The Delta with respect to stock B, for a correlation of zero is -0.3189.

Input Arguments

collapse all

Annualized, continuously compounded rate term structure, specified using intenvset.

Data Types: structure

Stock specification for asset 1, specified using stockspec.

Data Types: structure

Stock specification for asset 2, specified using stockspec.

Data Types: structure

Settlement or trade dates, specified as an NINST-by-1 vector of numeric dates.

Data Types: double

Maturity dates, specified as an NINST-by-1 vector.

Data Types: double

Option type, specified as an NINST-by-1 cell array of character vectors with a value of 'call' or 'put'.

Data Types: cell

Strike prices, specified as an NINST-by-1 vector.

Data Types: double

Correlation between the underlying asset prices, specified as an NINST-by-1 vector.

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [PriceSens] = minassetsensbystulz(RateSpec, StockSpecA,StockSpecB,Settle,Maturity,OptSpec,Strike,Corr,'OutSpec',OutSpec)

Define outputs, specified as the comma-separated pair consisting of 'OutSpec' and a NOUT- by-1 or 1-by-NOUT cell array of character vectors or string array with possible values of 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', and 'All'.

OutSpec = {'All'} specifies that the output is Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec to include each sensitivity:

Example: OutSpec = {'delta','gamma','vega','lambda','rho','theta','price'}

Data Types: cell

Output Arguments

collapse all

Expected prices or sensitivities, returned as an NINST-by-1 or NINST-by-2 vector.

Introduced in R2009a