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Option Pricing Junya Namai
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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
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Current Option Price for Netflix http://finance.yahoo.com/q/op?s=NFLX&m=2013-05 http://finance.yahoo.com/q/op?s=NFLX&m=2013-05
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Binomial Model for Stock t0t0 t1t1 up down $80 $55 P(u) = 0.6 P(d) = 0.4 r = 0.08
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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)
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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)
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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 = 0.08 0.6 0.4 0.6 $20 $10 $0 Max(0, Price-K)
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Call Option - Multi Period t4t4 $90 $80 $70 $60 $50 Path 1 4 6 4 1 call $20 $10 $0 4ups 3ups + 1down 2ups + 2downs 3downs + 1up 4downs
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Call Option - Multi Period
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Binomial Distribution (Pascal's triangle)
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Black-Scholes Formula (5 parameters) Stock Price Exercise (Strike) Price Time to Expiration Volatility of Stock Risk-Free Rate
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Black-Scholes Formula
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Binomial vs Black-Scholes Binomial Flexible Finite steps Discrete Values American Values complexities Black-Scholes Limited Infinite Continuous
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Quick Quiz 1 If volatility of stock price becomes higher, does the option price go up or down? Black-Scholes Calculator Black-Scholes Calculator
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Lognormal Distribution
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Quick Quiz 2 If interest rates becomes higher, does the option price go up or down?
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Question
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Reference http://stattrek.com/probability-distributions/binomial.aspx http://stattrek.com/probability-distributions/binomial.aspx http://en.wikipedia.org/wiki/Binomial_distribution 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://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://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://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://easycalculation.com/statistics/binomial-distribution.php http://www.hoadley.net/options/bs.htm http://www.hoadley.net/options/bs.htm
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Risk-Neutral Valuation (Backup)
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Up and Down Changes to STD
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