sttsens

Instrument sensitivities and prices using standard trinomial tree

Syntax

[Delta,Gamma,Vega,Price] = sttsens(STTTree,InstSet)

[Delta,Gamma,Vega,Price] = sttsens(___,Name,Value)

Description

[Delta,Gamma,Vega,Price] = sttsens(STTTree,InstSet) to generate instrument sensitivities and prices using a standard trinomial (STT) tree.

[Delta,Gamma,Vega,Price] = sttsens(___,Name,Value) to generate instrument sensitivities and prices using a standard trinomial (STT) tree with an optional name-value pair argument for Options.

Examples

Determine the Price and Sensitivities for a stttree Instrument Set

Load the data into the MATLAB® workspace.

load deriv.mat

STTTree and STTInstSet are the input arguments required to call the function sttprice. Use the command instdisp to examine the set of instruments contained in the variable STTInstSet.

instdisp(STTInstSet)

Index Type     OptSpec Strike Settle         ExerciseDates  AmericanOpt Name  Quantity
1     OptStock call    100    01-Jan-2009    01-Jan-2011    1           Call1 10      
2     OptStock put      80    01-Jan-2009    01-Jan-2012    0           Put1   5      
 
Index Type    OptSpec Strike Settle         ExerciseDates  AmericanOpt BarrierSpec Barrier Rebate Name     Quantity
3     Barrier call    105    01-Jan-2009    01-Jan-2012    1           ui          115     0      Barrier1 1       
 
Index Type     UOptSpec UStrike USettle        UExerciseDates UAmericanOpt COptSpec CStrike CSettle        CExerciseDates CAmericanOpt Name      Quantity
4     Compound call     95      01-Jan-2009    01-Jan-2012    1            put      5       01-Jan-2009    01-Jan-2011    1            Compound1 3       
 
Index Type     OptSpec Strike Settle         ExerciseDates  AmericanOpt Name      Quantity
5     Lookback call    90     01-Jan-2009    01-Jan-2012    0           Lookback1 7       
6     Lookback call    95     01-Jan-2009    01-Jan-2013    0           Lookback2 9       
 
Index Type  OptSpec Strike Settle         ExerciseDates  AmericanOpt AvgType    AvgPrice AvgDate Name   Quantity
7     Asian call    100    01-Jan-2009    01-Jan-2012    0           arithmetic NaN      NaN     Asian1 4       
8     Asian call    100    01-Jan-2009    01-Jan-2013    0           arithmetic NaN      NaN     Asian2 6       
 

The instrument set contains eight instruments:

• Two vanilla options (Call1, Put1)

• One barrier option (Barrier1)

• One compound option (Compound1)

• Two lookback options (Lookback1, Lookback2)

• Two Asian options (Asian1, Asian2)

Use sttsens to calculate the price and sensitivities for each instrument in the instrument set.

[Delta,Gamma,Vega,Price] = sttsens(STTTree, STTInstSet)

Delta = 8×1

    0.5267
   -0.0943
    0.4726
   -0.0624
    0.2313
    0.3266
    0.5706
    0.6646

Gamma = 8×1
105 ×

    0.0000
    0.0000
    0.0000
    0.0000
   -1.8650
   -1.9119
    1.8650
    1.9119

Vega = 8×1

   52.8980
   42.4369
   25.9792
   -9.5266
   70.3758
   92.9226
   25.8122
   37.8757

Price = 8×1

    4.5025
    3.0603
    3.7977
    1.7090
   11.7296
   12.9120
    1.6905
    2.6203

Determine Price and Sensitivities for Convertible Bond Instruments Using a stttree

Create a RateSpec.

StartDates = 'Jan-1-2015'; 
EndDates = 'Jan-1-2020'; 
Rates = 0.025; 
Basis = 1; 

RateSpec = intenvset('ValuationDate',StartDates,'StartDates',StartDates,...
'EndDates',EndDates,'Rates',Rates,'Compounding',-1,'Basis',Basis)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.8825
            Rates: 0.0250
         EndTimes: 5
       StartTimes: 0
         EndDates: 737791
       StartDates: 735965
    ValuationDate: 735965
            Basis: 1
     EndMonthRule: 1

Create a StockSpec.

AssetPrice = 80; 
Sigma = 0.12; 
StockSpec = stockspec(Sigma,AssetPrice)

StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1200
         AssetPrice: 80
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Create a STTTree.

TimeSpec = stttimespec(StartDates, EndDates, 20);
STTTree = stttree(StockSpec, RateSpec, TimeSpec)

STTTree = struct with fields:
       FinObj: 'STStockTree'
    StockSpec: [1x1 struct]
     TimeSpec: [1x1 struct]
     RateSpec: [1x1 struct]
         tObs: [1x21 double]
         dObs: [1x21 double]
        STree: {1x21 cell}
        Probs: {1x20 cell}

Define the convertible bond. The convertible bond can be called starting on Jan 1, 2016 with a strike price of 95.

CouponRate = 0.03;
Settle = 'Jan-1-2015'; 
Maturity = 'April-1-2018'; 
Period = 1;
CallStrike = 95; 
CallExDates = [datenum('Jan-1-2016') datenum('April-1-2018')];
ConvRatio = 1;
Spread = 0.025;

Price the convertible bond using the standard trinomial tree model.

[Price,PriceTree,EqtTre,DbtTree] = cbondbystt(STTTree,CouponRate,Settle,Maturity,ConvRatio,...
'Period',Period,'Spread',Spread,'CallExDates',CallExDates,'CallStrike',CallStrike,'AmericanCall', 1)

Price = 90.2511

PriceTree = struct with fields:
    FinObj: 'TrinPriceTree'
     PTree: {1x21 cell}
      tObs: [1x21 double]
      dObs: [1x21 double]

EqtTre = struct with fields:
    FinObj: 'TrinPriceTree'
     PTree: {1x21 cell}
      tObs: [1x21 double]
      dObs: [1x21 double]

DbtTree = struct with fields:
    FinObj: 'TrinPriceTree'
     PTree: {1x21 cell}
      tObs: [1x21 double]
      dObs: [1x21 double]

Compute the delta and gamma of the convertible bond.

InstSet= instcbond(CouponRate,Settle,Maturity,ConvRatio,'Spread',Spread,...
'CallExDates',CallExDates,'CallStrike',CallStrike,'AmericanCall',1);
[Delta,Gamma] = sttsens(STTTree,InstSet)

Delta = 0.3945

Gamma = 0.0324

Input Arguments

STTTree — Stock tree structure for standard trinomial tree

structure

Stock tree structure for a standard trinomial tree, specified by using stttree.

Data Types: struct

InstSet — Variable containing a collection instruments

structure

Variable containing a collection of NINST instruments, specified as a structure. Instruments are broken down by type and each type can have different data fields.

Data Types: struct

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: [Delta,Gamma,Vega,Price] = sttsens(STTTree,InstSet,'Options',deriv)

'Options' — Derivatives pricing options

structure

Derivatives pricing options, specified as the comma-separated pair consisting of 'Options' and a structure that is created with derivset.

Data Types: struct

Output Arguments

Delta — Rate of change of instruments prices with respect to changes in the stock price

vector of deltas

Rate of change of instrument prices with respect to changes in the stock price, returned as a NINST-by-1 vector of deltas. For more information on the stock tree, see stttree.

Gamma — Rate of change of instrument deltas with respect to changes in the stock price

vector of gammas

Rate of change of instrument deltas with respect to changes in the stock price, returned as a NINST-by-1 vector of gammas.

Vega — Rate of change of instrument prices with respect to changes in the volatility of the stock price

vector of vegas

Rate of change of instrument prices with respect to changes in the volatility of the stock price, returned as a NINST-by-1 vector of vegas. For more information on the stock tree, see stttree.

Price — Expected prices for each instrument at time 0

matrix

Expected prices for each instrument at time 0, returned as a NINST-by-1 vector. The prices are computed by backward dynamic programming on the standard trinomial (STT) stock tree. If an instrument cannot be priced, a NaN is returned in that entry.