Math 5076 Project 1
Transcript of Math 5076 Project 1
L o g o
L o g oTrinomial Tree vs. MC
Gopher 6 Consulting: Di(Emma) Wu and Zheng Rong
L o g oAgenda
AAPL stock and Option Price 1
Trinomial Tree & MC from Class2
Functions from Financial Toolbox 3
Comparison of Different Methods 4
L o g oAAPL and Option Price
❖Compare results by using different computational finance methods with the real option price of AAPL
▪All data come from real market data▪Researches include: Yahoo Finance &
S&P Capital IQ’s Stock Report & Thomson Reuters StockReports+
L o g oDiagram (Yahoo Finance)
Data from http://finance.yahoo.com/q?s=AAPL
Implied Volatility 25.05%
L o g oResearch Report
S&P Capital IQ
TargetPrice
Thomson StockReports+
L o g oRisk Free Interest Rate & Option
Risk Free Interest Rate: 13 WEEK TREASURY BILL (^IRX) 0.265 March 4
Choose 0.003Those tests are recommended if time allowed:● Sensitivity Test● Scenario Test ● Statistics Test
L o g oAssumptions we use
Implied σ=25.05%
S0=103 r=0.003
Sk=125
T=319 days
Call Option
Div & Yield=2.02%
L o g oAssumptions we use
Implied σ=27.86%
S0=103 r=0.003
Sk=125
T=319 days
Put Option
Div & Yield=2.02%
L o g o
Monte Carlo Simulationn
Strike price Bid price Ask price Implied Volatility Expire date
call 125 2.90 3.05 25.05% 20-Jan-2017
put 125 25.50 25.90 27.86% 20-Jan-2017
Results:
Call option: We get 3.0323.Put option: We get 25.4100.
L o g oImplied Trinomial Tree
Strike price Bid price Ask price Implied Volatility Expire date
call 125 2.90 3.05 25.05% 20-Jan-2017
put 125 25.50 25.90 27.86% 20-Jan-2017
Results:
Call option: We get 3.2297.Put option: We get 32.4783.
L o g oFunctions from Financial Toolbox
Generality
Robustness
Readability
stttree
StockSepcRateSpecSTTTimeSpec
More Flexibility
•Div•Rf•Structure •Track•Easy
Treeviewer
Standard Trinomial Tree
Usability
L o g oMy personal experience
Goole!Mathworks
Begin with Mimic
Algorithm
Data Structure
Search
Help
Edit
Toolbox
L o g oMatlab Code
Adjusted to Today’s Market Price Create a StockSpec:% Create a StockSpecAssetPrice=102.11;Sigma=0.2525;Div=0.0202;StockSpec=stockspec(Sigma,AssetPrice,'continuous',Div)
L o g oMatlab CodeAdjusted to Today’s Market Price% Create a RateSpecStartDates = 'Mar-7-2016';EndDates='Jan-20-2017';Rates=0.003;Basis=1; % Day count basis; 1 = 30/360 (SIA)Compounding=-1; % ?1 = Continuous compounding% Scalar value representing the rate at which the input% zero rates were compounded when annualized. Default is 2.RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates,
'EndDates', EndDates, 'Rates', Rates,'Compounding', Compounding, 'Basis', Basis)
L o g oMatlab Code% Create a
TimeSpecNumPeriods = 12;TimeSpec =
stttimespec(StartDates, EndDates, NumPeriods);
% Create a Standard
Trinomial TreeSTTTree=stttree(Stoc
kSpec, RateSpec, TimeSpec)
L o g oWait, this looks like black box!Not Really! Use edit functionFor example:
Readable Code and Adjustable!
% Calculate standard probs:Common = sqrt(dT/(12 *
Sigma0^2)) .* (BRates - (Sigma0^2)/2);
for iLevel=1:NumLevels-1 PTree{iLevel}(1,:) = 1/6 +
Common(iLevel); PTree{iLevel}(3,:) = 1/6 -
Common(iLevel); PTree{iLevel}(2,:) = 2/3;end
% Build Tree StructureSTTTree =
classfin('STStockTree');STTTree.StockSpec = StockSpec;STTTree.TimeSpec =
STTTimeSpec;STTTree.RateSpec =
RateSpecOri;STTTree.tObs = TreeTimes';STTTree.dObs = TreeDates';STTTree.STree = STree;STTTree.Probs = PTree;
L o g oOption Prices Vanilla OptionsSettle = '3/7/16';ExerciseDates = [datenum('1/20/17');datenum('1/20/17')];OptSpec = {'call';'put'};Strike =[125;75]; Price = optstockbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)P=0.30013Asian Options
Price = asianbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)
P=0.48820
LookBack OPtions Price= lookbackbystt(STTTree, OptSpec, Strike, Settle, ExerciseDates)
P=4.2269
Most Efficient : Use load deri.mat
L o g oComparison with Real Data Real Market Price Now:
Results From Matlab: P=3.0013Why Different? Change Too Quick! Highly Depend On Assumptions!
(Div & Yield, Risk-Free Interest, Volatility)
L o g oMonte Carlo Simulation_Antithetic
AssetPrice = 102.08;Sigma = 0.2512;StockSpec = stockspec(Sigma, AssetPrice)
StartDates = 'Mar-7-2016';EndDates = 'Jan-20-2017';Rates = 0.003-0.0202;RateSpec = intenvset('ValuationDate', StartDates, 'StartDates', StartDates, 'EndDates', EndDates, 'Rates', Rates)
OptSpec = 'call';Settle = 'Mar-7-2016';ExerciseDates = 'Jan-20-2017';Strike = 125;
RateSpec
Antithetic = true; Price = optstockbyls(RateSpec, StockSpec, OptSpec, Strike, Settle,ExerciseDates, 'Antithetic', Antithetic)
Price =2.8310
StockSpec
Vanilla Option
L o g oTable
Basic MC
Antithetic MC
Implied Trinomial Tree
Standard Trinomial Tree
Real price
Call 3.0323
2.8310 3.2297 3.0031 2.98
Put 25.4100
32.4763 25.50
L o g o
L o g o
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Gopher 6 Consulting