7/21/2019 Nick Stavrou Tutorial Questions 2015

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Tutorial Questions

Nick Stavrou Lectures 10, 11 &12

QUESTIONS FOR LECTURE 10

1. ABC is trading currently at 100. Assu!e a one "eriod Bino!ial #odel, t$at t$e stock"rice %ill eit$er go u" or do%n y 10' over t$e ne(t "eriod and t$e risk)*ree rate

over t$e "eriod is +' Take t$e "eriod to e a year-.

a- Build a re"licating "ort*olio to value a call o"tion %ritten today %it$ a

strike "rice o* 100. $at is t$e value $edge ratio

/

- Calculate t$e risk)neutral "roailities and value t$e call using t$e risk)

neutral "roailities. C$eck t$at you get t$e sa!e ans%er as in a. aove-c- sing t$e risk)neutral "roailities aove also calculate t$e value o* t$e

*ind t$e value o* a "ut o"tion %ritten today, lasting one "eriod, and %it$ an

e(ercise "rice o* 100.

d- eri*y t$at t$e sa!e "rice *or t$e "ut results *ro! "ut)call "arity.2. #icroso*t stock is currently trading at 1. Consider call and "ut o"tions %it$ a strike

o* 2.00 e("iring in 30 days 40.052 years-. Su""ose t$at t$e volatility o* #icroso*t

stock is 0' and t$at t$e interest rate is 3'. $at are t$e Black)Sc$oles "rices o*

t$e call and t$e "ut/ $at are t$e o"tion deltas/

QUESTIONS FOR LECTURE 11

1. T$is 6uestion re*ers to t$e volatility s!ile7

a- $at is t$e o"tion s!ile/- $y does it arise *ro! *at)tailed stock return distriutions/

c- A ske%ed i!"lied volatility s!ile occurs !ore o*ten t$an a sy!!etric s!ile in

e6uity !arkets. 8("lain/d- Su""ose t$at S&9 +00 o"tions dis"lay a s!ile %it$ an u"%ard ske% on t$e

le*t.

:* your vie% t$at t$e !arket $as overesti!ated cras$ risklarge negative

return- and t$e s!ile $as a ske% t$at is !uc$ stee"er t$an it s$ould e, %$at

o"tions trading strategy could you ado"t to "ro*it *ro! t$is/

2. T$is 6uestion re*ers to t$e various as"ects o* alue at ;isk a;-.a- $at are t$e t$ree di**erent a""roac$es to co!"uting a;/- State so!e advantages and disadvantages o* eac$ !et$od.c-

7/21/2019 Nick Stavrou Tutorial Questions 2015

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1. =ou are a desk 6uant and asked to "rice a t%o)year annual "ay!ent credit de*ault

s%a" C>S-. T$e !arket convention is to deter!ine and 6uote t$e C>S s"read

s.

T$e risk)*ree interest rate is *or t%o)years r=

10 . Su""ose t$e conditional

"roaility o* de*ault eac$ yearp

is also constant.

9lease *ind t$e relations$i" e("resses t$e t%o)year *air value C>S s"reads

in

ter!s o* ti!e to !aturity, recovery rate and notional value o* t$e contract.Assu!e t$at all de*ault "ay!ents are !ade at t$e end o* t$e "eriod, and all

"re!iu! "ay!ents are !ade at t$e eginning o* eac$ "eriod. Also assu!e t$at

recovery isR=40

o* notional value is 100.-

2. T$e #erton 1?@- !odel !ay e used to value onds %it$ de*ault risk in a

co!"any. 8("lain $o% det is vie%ed as an o"tion in t$is *ra!e%ork.