Option pricing
Download
1 / 23

Option Pricing - PowerPoint PPT Presentation


  • 140 Views
  • Uploaded on

Option Pricing. Junya Namai. Agenda. Current Option Price for Netflix Binomial Model for Stock Binomial Options P ricing for Call Option Binomial Options P ricing for Put Option Binomial Options P ricing for Call Option – Multi period Black-Scholes Model Quiz Questions.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Option Pricing' - laken


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Option pricing

Option Pricing

JunyaNamai


Agenda
Agenda

  • Current Option Price for Netflix

  • Binomial Model for Stock

  • Binomial Options Pricing for Call Option

  • Binomial Options Pricing for Put Option

  • Binomial Options Pricing for Call Option – Multi period

  • Black-Scholes Model

  • Quiz

  • Questions


Current option price for netflix
Current Option Price for Netflix

  • http://finance.yahoo.com/q/op?s=NFLX&m=2013-05


Binomial model for stock
Binomial Model for Stock

t0

t1

$80

P(u) = 0.6

up

P(d) = 0.4

down

$55

r = 0.08

= = $64.81


Binomial options pricing for call option
Binomial options pricing for Call Option

K = $70

t0

t1

Max(0, Price - K)

P(u) = 0.6

$10

$80

P(d) = 0.4

up

r = 0.08

down

$55

$0

= = $5.556


Binomial options pricing for put option
Binomial options pricing for Put Option

K = $70

t0

t1

Max(0, K-Price)

P(u) = 0.6

$0

$80

P(d) = 0.4

up

r = 0.08

down

$55

$15

= = $5.556


Call option multi period
Call Option - Multi Period

t0

t1

t2

t3

t4

Max(0, Price-K)

$20

$90

0.6

0.6

0.4

$10

$80

0.6

0.6

0.4

0.6

0.6

0.4

0.4

$70

$0

0.4

0.6

0.4

0.6

0.4

0.6

0.4

$0

K = $70

$60

0.6

P(u) = 0.6

0.4

r = 0.08

P(d) = 0.4

0.4

$0

$50


Call option multi period1
Call Option - Multi Period

Path

call

t4

1

4ups

$90

$20

4

3ups + 1down

$80

$10

6

$0

2ups + 2downs

$70

4

$60

$0

3downs + 1up

1

$0

$50

4downs


Call option multi period2
Call Option - Multi Period



Black scholes formula 5 parameters
Black-Scholes Formula (5 parameters)

  • Stock Price

  • Exercise (Strike) Price

  • Time to Expiration

  • Volatility of Stock

  • Risk-Free Rate


Black scholes formula
Black-Scholes Formula

  • Value of call option =

    • cumulative normal probability density function

    • = exercise price of option; PV(EX) is calculated by discounting at the risk-free interest rate rf

    • t = number of periods to exercise date

    • P = price of stock now

    • = standard deviation per period of (continuously compounded) rate of return on stock


Black scholes formula1
Black-Scholes Formula

  • P=430, EX=430, =0.4068, t=0.5(6 months), rf=.05

    • = = 0.1956

    • = 0.195 – 0.4068 = -0.0921

    • = N(-0.0921) = 1-N(0.0921) = 0.4633

      • Use Normsdist function in Excel

    • = 0.5775430 – (0.4633430/1.015) = 52.04

    • $52.04


Binomial vs black scholes
Binomial vs Black-Scholes

  • Binomial

    • Flexible

    • Finitesteps

    • Discrete

    • Values American

    • Values complexities

  • Black-Scholes

    • Limited

    • Infinite

    • Continuous


Quick quiz 1
Quick Quiz 1

  • If volatility of stock price becomes higher, does the option price go up or down?

  • Black-Scholes Calculator



Quick quiz 2
Quick Quiz 2

  • If interest rates becomes higher, does the option price go up or down?



Reference
Reference

  • http://stattrek.com/probability-distributions/binomial.aspx

  • http://en.wikipedia.org/wiki/Binomial_distribution

  • http://www.tradingtoday.com/black-scholes?callorput=c&strike=70&stock=70&time=180&volatility=48&interest=8

  • http://en.wikipedia.org/wiki/Binomial_options_pricing_model

  • http://www.optiontradingpedia.com/free_black_scholes_model.htm

  • http://www.optiontradingpedia.com/free_black_scholes_model.htm

  • http://easycalculation.com/statistics/binomial-distribution.php

  • http://www.hoadley.net/options/bs.htm


Risk neutral valuation backup
Risk-Neutral Valuation (Backup)

Expected return

rf = 1.5%

Expected return

1.5 = 33p - 25(1-p)

1.5 = 33p + 25p -25

p = 45.6%


Risk neutral valuation backup1
Risk-Neutral Valuation (Backup)


Risk neutral valuation backup2
Risk-Neutral Valuation (Backup)


Up and down changes to std
Up and Down Changes to STD

  • 1+upside change = u =

  • 1+downside change = d = 1/u

    • e = 2.718

    • = standard deviation of stock returns

    • h = interval as fraction of a year

  • To find the standard deviation given u, we turn the formula around


ad