Option Pricing Junya Namai. Agenda  Current Option Price for Netflix  Binomial Model for Stock  Binomial Options Pricing for Call Option  Binomial.

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Presentation transcript:

Option Pricing Junya Namai

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 

Binomial Model for Stock t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 r = 0.08

Binomial options pricing for Call Option t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 K = $70 $10 $0 r = 0.08 Max(0, Price - K)

Binomial options pricing for Put Option t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 K = $70 $0 $15 r = 0.08 Max(0, K-Price)

Call Option - Multi Period t0t0 t1t1 t2t2 t3t3 t4t4 $90 $80 $70 $60 $50 P(u) = 0.6 P(d) = 0.4 K = $70 r = $20 $10 $0 Max(0, Price-K)

Call Option - Multi Period t4t4 $90 $80 $70 $60 $50 Path call $20 $10 $0 4ups 3ups + 1down 2ups + 2downs 3downs + 1up 4downs

Call Option - Multi Period

Binomial Distribution (Pascal's triangle)

Black-Scholes Formula (5 parameters)  Stock Price  Exercise (Strike) Price  Time to Expiration  Volatility of Stock  Risk-Free Rate

Black-Scholes Formula

Binomial vs Black-Scholes  Binomial  Flexible  Finite steps  Discrete  Values American  Values complexities  Black-Scholes  Limited  Infinite  Continuous

Quick Quiz 1  If volatility of stock price becomes higher, does the option price go up or down?  Black-Scholes Calculator Black-Scholes Calculator

Lognormal Distribution

Quick Quiz 2  If interest rates becomes higher, does the option price go up or down?

Question

Reference    scholes?callorput=c&strike=70&stock=70&time=180&volatility =48&interest=8 scholes?callorput=c&strike=70&stock=70&time=180&volatility =48&interest=8     

Risk-Neutral Valuation (Backup)

Up and Down Changes to STD