New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Managing Financial Risk Week VI Notes

by: Kwan

Managing Financial Risk Week VI Notes BU.230.730.53.SP16

Marketplace > Johns Hopkins University > Finance > BU.230.730.53.SP16 > Managing Financial Risk Week VI Notes

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Options Management
Managing Financial Risk
Nicola Fusari
Class Notes
25 ?




Popular in Managing Financial Risk

Popular in Finance

This 9 page Class Notes was uploaded by Kwan on Thursday April 28, 2016. The Class Notes belongs to BU.230.730.53.SP16 at Johns Hopkins University taught by Nicola Fusari in Spring 2016. Since its upload, it has received 37 views. For similar materials see Managing Financial Risk in Finance at Johns Hopkins University.


Reviews for Managing Financial Risk Week VI Notes


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 04/28/16
Risk  VI Tuesday,  April  26,  2016 13:37 •1.  Assignment <-­‐-­‐ How  to  prepare  Final &  Formulas:  cheat  sheet  (posted) A  conference:  The  role  of  derivatives  in  asset  pricing:  June  4,  2016  (Baltimore,   MD) A  dinner Audio  recording  started:  13:40  Wednesday,  April  27,  2016 Assignment 1) Rt  ~  N  (miu,  sigma)  -­‐-­‐ average  Rt;  stdev  Rt Unconditional  (the  same  sigma):   (Rt-­‐miu)/sigma  ~N  (0,1) Sorted  return:  =small Normal  Quantile:  =quantile  (array,  1/3520) Compare:  plot  (tails  are  not  normal  distribution) Conditional Rt/sigma-­‐t    =  zt Rt  ~  N  (0,  sigma-­‐t) Is  z  normal  distribution Sigma-­‐t:  ghost  (RM  <  GARCH  <  RV:  normal) If  RM/GARCH  ,  compensate:  zt  -­‐-­‐ fat  tail,  t-­‐student 2) d? Method  of  Moments (4th  moment) If  RM/GARCH  ,  compensate:  zt  -­‐-­‐ fat  tail,  t-­‐student 2) d? Method  of  Moments (4th  moment) Data                                                                  Model Ex.  Kurt  (zs)                                        Ex.  Kurt=6/(d -­‐4) Ri/sigma-­‐i  =  zi =kurt(array) Compare:  if  kurt  =  0,  normal  (d  -­‐-­‐>  infinite) T.INV  (p,  d)                                           TINV  (p,  d)   t-­‐student:  one  tail                  Two  tails Negative                                                    Positive                                                                                     =-­‐TINV(2*p,  d) FHS:  (only  t+1) -­‐2:  possibility  1/4 VaR=  -­‐2*sigma_t+1 -­‐2  =  percentile  (zs,  0.25)  or  =  percentile  (array,  0.01) 4) Which  is  better? HS,  Normal  Distribution,  t-­‐student,  FHS How  many  times  actual  loss  larger  than  VaR  (violations): =if  [It  =  1  if  loss  >=  VaR,  else    0:  ∏(1-­‐tao)^(1-­‐It)*tau^It] L(^tau)=(1-­‐^tao)^T0*^tao^T1 -­‐2  =  percentile  (zs,  0.25)  or  =  percentile  (array,  0.01) 4) Which  is  better? HS,  Normal  Distribution,  t-­‐student,  FHS How  many  times  actual  loss  larger  than  VaR  (violations): =if  [It  =  1  if  loss  >=  VaR,  else    0:  ∏(1-­‐tao)^(1-­‐It)*tau^It] L(^tau)=(1-­‐^tao)^T0*^tao^T1 L(p)=(1-­‐p)^T0*^p^T1 L(p)=<  L(^tau);  as  ^tao  the  maximum 2 -­‐2*ln(L(p)/L(^tau))>=0  ~  ???? P=0.01,  total=754 tau  compared  with  p 5) Monte  Carlo  Simulation: 1st  Matrix:  random  numbers  from  normal  distribution Multiply Compute  average -­‐-­‐>  Crystal  ball 1st  Matrix:  random  numbers  from  normal  distribution Multiply Compute  average -­‐-­‐>  Crystal  ball FHS:  only  z  differs Only  1st  Matrix  changes:  =  index(array  of  past  zs,  Ceil(Rand()*500):  #  1~ 500) •2.  Options Risk  Management Lec 6 1) Black-­‐Scholes :  50  years Assumptions:  ……sigma  as  constant…. Can  replicate  any  portfolio  in  the  future:  market  is  complete miu  =  Rf e Rt+T=e ln(St+T/St) E(X):  expected  value  (continuous,  like  ∑) If  Rt+1  ~  t-­‐student Sigma_t+1   -­‐-­‐>  GARCH -­‐-­‐>  Use  Monte  Carlo  Simulation 2) Implied  volatility: C  =  BS  (St,  K,  T,  rf,  d,  sigma)  &  put-­‐call  parity  for  Put <-­‐-­‐ But  market:  "-­‐-­‐>"  as  Demand  &  supply  $;  thus  sigma Eg.  25=BS(1000,1000,1m,0.05,2%,  ?);  sigma  =  0.15  -­‐-­‐>  cheap,  sigma  =  0.7  -­‐-­‐>   expensive If  BS  true  -­‐-­‐>  Implied  Volatility  Surface Market  changed: Oct26,  1987:  S&P  sharp  down,  no  longer  a  level  plane  -­‐-­‐>  put  option,  higher   price,  more  expensive More  options Possible  model  extensions t  (today):  buy  call  oppion  Ct  =(St,  K,  t,  sigma..)  -­‐-­‐>  t+1  Ct+1  =(St+1,  K,  T,  sigma) Risk:  Ct+1  -­‐ Ct   t+1‐-(percentile):  unknown Rt+1~  N(0,  sigma):  known Ct+1=f(Rt+1)  ? t  (today):  buy  call  option  Ct  =(St,  K,  t,  sigma..)  -­‐-­‐>  t+1  Ct+1  =(St+1,  K,  T,  sigma) p Risk:  Ct+1  -­‐ Ct   t+1‐-(percentile):  unknown Rt+1~  N(0,  sigma):  known Ct+1=f(Rt+1)  ? 3) Greeks Delta: c(St+1)  =  c(St)  +  δ8 \*(St+1  -­‐St)  *St/St (St+1  -­‐ St)  /St  =  rt+1  (simple  return)   ≈ Rt Ct+1  -­‐Ct  ≈ δ*Rt+1*St NB.  X~N(0,δ)  -­‐-­‐>  aX  ~  N(0,  a δ ) VaR:  approximation  (not  good)  :  where  differences  are  large  is  used Gamma:  Taylor  expansion Better  approximation With  uncertain  chi  distributio-­‐-­‐  > 4) Full  Valuation  (Monte  Carlo  Simulation): BS:  easy  cuz Ct  is  easy t  -­‐-­‐>  t+T  (sigma  constant) Ct  is  easy t  -­‐-­‐>  t+T  (sigma  constant) (Final  -­‐-­‐easier) 5) Excel: Options:  365 Volatility:  252 -­‐-­‐>  change  sigma  to  calendar  day Delta=N(d1) Delta-­‐Approx:   Full  Valuation  (Monte  Carlo): Visual  Basic:  to  define  BS  formula -­‐-­‐Trajectories -­‐-­‐Percentile [book]


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Amaris Trozzo George Washington University

"I made $350 in just two days after posting my first study guide."

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.