Question
WordgetsoutthatyouaredoingsuchagreatjobinyournewroleandsoitisnotlongbeforeyouareaskedbacktoUTStogiveaguestlecture(viaZoom).Thesubjectcoordinatorhasaskedyoutohelpwithsomeofthetrickieraspectsoflectures8,9,and10ofDerivativeSecurities(25620).Specifically,youhavebeenaskedtogothroughthecalculationofvariousoptionpricesusingbothbinomialtreesandtheBlackScholesmodel.Theexampletobeusedisasfollows:Astockiscurrentlytradingat$14.56andhasavolatilityof32%perannumandacontinuousdividendyieldof1.30%perannumwithcontinuouscompounding.Theriskfreeinterestrateis2.51%perannumwithcontinuouscompoundingforallmaturities.Givenyourexpertiseinstockoptionvaluationyoudecidetouseafourstepbinomialtreetocalculatethefollowingderivativeprices(tofourdecimalplaces):(a) AoneyearEuropeanputoptionwithastrikeof$15.00.CalculatealsothevalueoftheoptionbyusingtheBlackScholesformula.Compareandcomment.(b) AoneyearAmericanputoptionwithastrikeof$15.00.Istheanswerdifferenttotheanswerfrom(a)?Explain.(c) Ashortpositioninaforwardcontractonthestockfordeliveryinoneyearatapriceof$15.00.Calculatealsothetheoreticalvalueoftheforwardcontract.Compareandcomment.(Hint:thefairforwardpricethatwouldbeagreedfornewcontractstodayisaround$16.71$15.00,hencetheforwardcontractinquestionhasanonzerovalue.)(d) AEuropeanupandoutbarrierputoptionwithastrikeof$15.00andknockoutbarrierof$17.00maturinginoneyear.Anupandoutputoptiongivestheholdertherighttoselltheunderlyingassetatthestrikepriceontheexpirationdatesolongasthepriceofthatassetdidnotgoaboveapredeterminedbarrierduringtheoption'slifetime.Whenthepriceoftheunderlyingassetrisesabovethebarrier,theoptionisknockedoutandnolongercarriesanyvalue.Commentonthepriceofthisoptionrelativetotheoptionin(a)andexplainanydifferences.
WordgetsoutthatyouaredoingsuchagreatjobinyournewroleandsoitisnotlongbeforeyouareaskedbacktoUTStogiveaguestlecture(viaZoom).Thesubjectcoordinatorhasaskedyoutohelpwithsomeofthetrickieraspectsoflectures8,9,and10ofDerivativeSecurities(25620).Specifically,youhavebeenaskedtogothroughthecalculationofvariousoptionpricesusingbothbinomialtreesandtheBlackScholesmodel.Theexampletobeusedisasfollows:Astockiscurrentlytradingat$14.56andhasavolatilityof32%perannumandacontinuousdividendyieldof1.30%perannumwithcontinuouscompounding.Theriskfreeinterestrateis2.51%perannumwithcontinuouscompoundingforallmaturities.Givenyourexpertiseinstockoptionvaluationyoudecidetouseafourstepbinomialtreetocalculatethefollowingderivativeprices(tofourdecimalplaces):(a) AoneyearEuropeanputoptionwithastrikeof$15.00.CalculatealsothevalueoftheoptionbyusingtheBlackScholesformula.Compareandcomment.(b) AoneyearAmericanputoptionwithastrikeof$15.00.Istheanswerdifferenttotheanswerfrom(a)?Explain.(c) Ashortpositioninaforwardcontractonthestockfordeliveryinoneyearatapriceof$15.00.Calculatealsothetheoreticalvalueoftheforwardcontract.Compareandcomment.(Hint:thefairforwardpricethatwouldbeagreedfornewcontractstodayisaround$16.71$15.00,hencetheforwardcontractinquestionhasanonzerovalue.)(d) AEuropeanupandoutbarrierputoptionwithastrikeof$15.00andknockoutbarrierof$17.00maturinginoneyear.Anupandoutputoptiongivestheholdertherighttoselltheunderlyingassetatthestrikepriceontheexpirationdatesolongasthepriceofthatassetdidnotgoaboveapredeterminedbarrierduringtheoption'slifetime.Whenthepriceoftheunderlyingassetrisesabovethebarrier,theoptionis"knockedout"andnolongercarriesanyvalue.Commentonthepriceofthisoptionrelativetotheoptionin(a)andexplainanydifferences.
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Fundamentals of Investments Valuation and Management
Authors: Bradford Jordan, Thomas Miller
7th edition
ISBN: 978-0078096785, 78096782, 978-0077861636, 77861639, 978-0078115660
