Class: Math::Greeks::Calculator

Inherits:
Object
  • Object
show all
Defined in:
lib/greeks.rb

Defined Under Namespace

Classes: GreekCalculations, NilMath

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(opts) ⇒ Calculator

Returns a new instance of Calculator.



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# File 'lib/greeks.rb', line 39

def initialize(opts)
  @stock_price                   = opts[:stock_price]
  @stock_dividend_rate           = opts[:stock_dividend_rate]
  @option_type                   = opts[:option_type]
  @option_price                  = opts[:option_price]
  @option_strike                 = opts[:option_strike]
  @option_expires_in_days        = opts[:option_expires_in_days]
  @federal_reserve_interest_rate = opts[:federal_reserve_interest_rate]
  
  @federal_reserve_interest_rate_f = federal_reserve_interest_rate / 100.0
  @stock_dividend_rate_f           = stock_dividend_rate / 100.0
  @option_expires_pct_year         = (option_expires_in_days + 1.0) / 365.0
  @option_expires_pct_year_sqrt    = Math.sqrt(option_expires_pct_year)
  
  
  @price_vs_rate_vs_expires = GreekCalculations.misc_price_vs_rate_vs_expires(
    :stock_price             => stock_price,
    :stock_dividend_rate_f   => stock_dividend_rate_f,
    :option_expires_pct_year => option_expires_pct_year
  )

  @rate_vs_expires = GreekCalculations.misc_rate_vs_expires(
    :option_expires_pct_year => option_expires_pct_year, 
    :stock_dividend_rate_f   => stock_dividend_rate_f
  )
  
  @strike_vs_fed_vs_expires = GreekCalculations.misc_strike_vs_fed_vs_expires(
    :option_strike                   => option_strike,
    :option_expires_pct_year         => option_expires_pct_year, 
    :federal_reserve_interest_rate_f => federal_reserve_interest_rate_f
  )
  
  @price_ratio_log_less_rates = GreekCalculations.misc_price_ratio_log_less_rates(
    :stock_price                     => stock_price, 
    :stock_dividend_rate_f           => stock_dividend_rate_f, 
    :option_strike                   => option_strike, 
    :option_expires_pct_year         => option_expires_pct_year, 
    :federal_reserve_interest_rate_f => federal_reserve_interest_rate_f
  )
end

Instance Attribute Details

#federal_reserve_interest_rate ⇒ Object (readonly)

Returns the value of attribute federal_reserve_interest_rate.



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# File 'lib/greeks.rb', line 27

def federal_reserve_interest_rate
  @federal_reserve_interest_rate
end

#federal_reserve_interest_rate_f ⇒ Object (readonly)

Returns the value of attribute federal_reserve_interest_rate_f.



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# File 'lib/greeks.rb', line 32

def federal_reserve_interest_rate_f
  @federal_reserve_interest_rate_f
end

#option_expires_in_days ⇒ Object (readonly)

Returns the value of attribute option_expires_in_days.



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# File 'lib/greeks.rb', line 26

def option_expires_in_days
  @option_expires_in_days
end

#option_expires_pct_year ⇒ Object (readonly)

Returns the value of attribute option_expires_pct_year.



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# File 'lib/greeks.rb', line 29

def option_expires_pct_year
  @option_expires_pct_year
end

#option_expires_pct_year_sqrt ⇒ Object (readonly)

Returns the value of attribute option_expires_pct_year_sqrt.



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# File 'lib/greeks.rb', line 30

def option_expires_pct_year_sqrt
  @option_expires_pct_year_sqrt
end

#option_price ⇒ Object (readonly)

bid, mid, or ask



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# File 'lib/greeks.rb', line 24

def option_price
  @option_price
end

#option_strike ⇒ Object (readonly)

Returns the value of attribute option_strike.



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# File 'lib/greeks.rb', line 25

def option_strike
  @option_strike
end

#option_type ⇒ Object (readonly)

:call, or :put



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# File 'lib/greeks.rb', line 23

def option_type
  @option_type
end

#price_ratio_log_less_rates ⇒ Object (readonly)

Returns the value of attribute price_ratio_log_less_rates.



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# File 'lib/greeks.rb', line 36

def price_ratio_log_less_rates
  @price_ratio_log_less_rates
end

#price_vs_rate_vs_expires ⇒ Object (readonly)

Returns the value of attribute price_vs_rate_vs_expires.



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# File 'lib/greeks.rb', line 34

def price_vs_rate_vs_expires
  @price_vs_rate_vs_expires
end

#rate_vs_expires ⇒ Object (readonly)

Returns the value of attribute rate_vs_expires.



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# File 'lib/greeks.rb', line 33

def rate_vs_expires
  @rate_vs_expires
end

#stock_dividend_rate ⇒ Object (readonly)

Returns the value of attribute stock_dividend_rate.



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# File 'lib/greeks.rb', line 22

def stock_dividend_rate
  @stock_dividend_rate
end

#stock_dividend_rate_f ⇒ Object (readonly)

Returns the value of attribute stock_dividend_rate_f.



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# File 'lib/greeks.rb', line 31

def stock_dividend_rate_f
  @stock_dividend_rate_f
end

#stock_price ⇒ Object (readonly)

Returns the value of attribute stock_price.



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# File 'lib/greeks.rb', line 21

def stock_price
  @stock_price
end

#strike_vs_fed_vs_expires ⇒ Object (readonly)

Returns the value of attribute strike_vs_fed_vs_expires.



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# File 'lib/greeks.rb', line 35

def strike_vs_fed_vs_expires
  @strike_vs_fed_vs_expires
end

Instance Method Details

#annualized_premium_value ⇒ Object

Annualized Premium The annualized premium is the value of the option divided by the strike price. You can use annualized premium to develop an intuitive understanding of how much the market is “paying” for a dollar of risk. For example, if a stock is trading at $50 and you sell a $50 strike 6 month call for $4, you are getting paid 8% in 6 months, or about 16% annualized, in exchange for being willing to buy at $50, the current price.



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# File 'lib/greeks.rb', line 137

def annualized_premium_value
  @annualized_premium_value ||= GreekCalculations.annualized_premium_value(
    :option_price            => option_price,
    :option_strike           => option_strike,
    :option_expires_pct_year => option_expires_pct_year
  )
end

#annualized_time_value ⇒ Object

Annualized Time Value The time value of the option divided by the strike price, then annualized. You can use annualized time value to develop an intuitive understanding of how much value the option market is adding to an in-the-money option beyond the intrinsic value. For example, if a stock is trading at $40 and a six month call on that stock with a strike price of $35 has an intrinsic value of $5 and a total value of $7, the time value ($2) divided by the strike is ($2/$40) = 5%. Annualizing that time value to a one year horizon on a continuously compounded basis yields 9.76% (2 × ln(1 + 0.05)).



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# File 'lib/greeks.rb', line 153

def annualized_time_value
  @annualized_time_value ||= GreekCalculations.annualized_time_value(
    :time_value              => time_value,
    :option_strike           => option_strike,
    :option_expires_pct_year => option_expires_pct_year
  )
end

#break_even ⇒ Object

Chance of Breakeven The probability that a stock will be trading beyond the breakeven price as implied by the option price. Chance of Breakeven can be used to get a sense for the valuation of the option by comparing the markets’ estimate of Chance of Breakeven to estimates derived from your own fundamental research. If you believe the Chance of Breakeven is less than the probability that a stock will be beyond the breakeven price at option expiration, then you believe the option is undervalued, and visa versa.



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# File 'lib/greeks.rb', line 87

def break_even
  @break_even ||= GreekCalculations.break_even(
    :stock_price                     => stock_price, 
    :stock_dividend_rate_f           => stock_dividend_rate_f, 
    :federal_reserve_interest_rate_f => federal_reserve_interest_rate_f, 
    :option_type                     => option_type, 
    :option_price                    => option_price, 
    :option_strike                   => option_strike, 
    :option_expires_pct_year         => option_expires_pct_year, 
    :option_expires_pct_year_sqrt    => option_expires_pct_year_sqrt, 
    :iv                              => iv
  )
end

#delta ⇒ Object

Delta A measurement of the change in the price of an option resulting from a change in the price of the underlying security. Delta is positive for calls and negative for puts. Delta can be calculated as the dollar change of the option that an investor can expect for a one-dollar change in the underlying security. For example, let’s say an option on a stock trading at $50 costs $1 and has a delta of $0.50 per dollar of underlying stock price change. If the stock price rises to $52, the price of the option will increase by $1 (the $2 price change times the $0.50 delta). After the stock price movement, the option will be worth $2 ($1 initial cost plus $1 delta). Delta can also be calculated as a percentage change in the option price for a one-percent change in the underlying security; this method of viewing the delta value is also known as “leverage.”



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# File 'lib/greeks.rb', line 201

def delta
  @delta ||= GreekCalculations.delta(
    :option_type            => option_type, 
    :iv                     => iv,
    :rate_vs_expires        => rate_vs_expires, 
    :d1_normal_distribution => d1_normal_distribution
  )
end

#gamma ⇒ Object

Gamma A measurement of the change in delta as the price of the underlying stock changes. As the underlying stock price changes, the delta of the option changes, too. Gamma indicates how quickly your exposure to the price movement of the underlying security changes as the price of the underlying security varies. For example, if you have a call with a strike of $50 and the stock price is $50, the delta likely will be approximately $0.50 for a one-dollar movement of the stock. At a stock price of $60, the delta will be greater, closer to $0.75. At a stock price of $40, the delta will be less, closer to $0.25. In this example, if the stock price changes from $50 to $60, then the delta will change from $0.50 to $0.75. The $10 change in stock price caused a $0.25 change in delta, so gamma is approximately $0.25/10, or $0.025, in this case.



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# File 'lib/greeks.rb', line 219

def gamma
  @gamma ||= GreekCalculations.gamma(
    :stock_price                  => stock_price, 
    :option_expires_pct_year_sqrt => option_expires_pct_year_sqrt, 
    :iv                           => iv, 
    :nd1                          => nd1, 
    :rate_vs_expires              => rate_vs_expires
  )
end

#iv ⇒ Object

Implied Volatility A measure of the “riskiness” of the underlying security. Implied volatility is the primary measure of the “price” of an option–how expensive it is relative to other options. It is the “plug” value in option pricing models (the only variable in the equation that isn’t precisely known). The remaining variables are option price, stock price, strike price, time to expiration, interest rate, and estimated dividends. Therefore, the implied volatility is the component of the option price that is determined by the market. Implied volatility is greater if the future outcome of the underlying stock price is more uncertain. All else equal, the wider the market expects the range of possible outcomes to be for a stock’s price, the higher the implied volatility, and the more expensive the option.



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# File 'lib/greeks.rb', line 171

def iv
  @iv ||= GreekCalculations.iv(
    :stock_price                     => stock_price,
    :stock_dividend_rate             => stock_dividend_rate,
    :stock_dividend_rate_f           => stock_dividend_rate_f,
    :option_type                     => option_type,
    :option_price                    => option_price,
    :option_strike                   => option_strike,
    :option_expires_in_days          => option_expires_in_days,
    :option_expires_pct_year         => option_expires_pct_year,
    :option_expires_pct_year_sqrt    => option_expires_pct_year_sqrt,
    :federal_reserve_interest_rate   => federal_reserve_interest_rate,
    :federal_reserve_interest_rate_f => federal_reserve_interest_rate_f,
    :price_ratio_log_less_rates      => price_ratio_log_less_rates,
    :rate_vs_expires                 => rate_vs_expires,
    :strike_vs_fed_vs_expires        => strike_vs_fed_vs_expires,
    :price_vs_rate_vs_expires        => price_vs_rate_vs_expires,
  )
end

#premium_value ⇒ Object

Intrinsic Value The value that the option would pay if it were executed today. For example, if a stock is trading at $40, a call on that stock with a strike price of $35 would have $5 of intrinsic value ($40-$35) if it were exercised today. However, the call should actually be worth more than $5 to account for the value of the chance of any further appreciation until expiration, and the difference between the price and the intrinsic value would be the time value.



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# File 'lib/greeks.rb', line 108

def premium_value
  @premium_value ||= GreekCalculations.premium_value(
    :option_type   => option_type,
    :option_strike => option_strike,
    :stock_price   => stock_price
  )
end

#rho ⇒ Object

Rho The change in the value of an option for a change in the prevailing interest rate that matches the duration of the option, all else held equal. Generally rho is not a big driver of price changes for options, as interest rates tend to be relatively stable.



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# File 'lib/greeks.rb', line 249

def rho
  @rho ||= GreekCalculations.rho(
    :option_type              => option_type, 
    :option_expires_pct_year  => option_expires_pct_year, 
    :strike_vs_fed_vs_expires => strike_vs_fed_vs_expires, 
    :d2_normal_distribution   => d2_normal_distribution,
    :iv                       => iv
  )
end

#theta ⇒ Object

Theta The change in an option’s value that an investor can expect from the passage of one day, assuming nothing else changes. Theta can be calculated in two ways, as the dollar change of the option that an investor can expect for a one-day passage of time, all else remaining equal, or as a percentage change in the option price for a one-day passage of time, all else remaining equal. For example, if an option trades at $1 on Monday morning and it has a theta of -$0.10 per day, you can expect the option to trade at $0.90 on Tuesday morning. Another way of measuring theta for that option is ($0.90 - $1)/$1 or -10% per day.



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# File 'lib/greeks.rb', line 266

def theta
  @theta ||= GreekCalculations.theta(
    :federal_reserve_interest_rate_f => federal_reserve_interest_rate_f, 
    :stock_dividend_rate_f           => stock_dividend_rate_f, 
    :option_type                     => option_type, 
    :option_expires_pct_year_sqrt    => option_expires_pct_year_sqrt, 
    :strike_vs_fed_vs_expires        => strike_vs_fed_vs_expires, 
    :price_vs_rate_vs_expires        => price_vs_rate_vs_expires, 
    :price_ratio_log_less_rates      => price_ratio_log_less_rates,
    :iv                              => iv, 
    :nd1                             => nd1, 
    :d1_normal_distribution          => d1_normal_distribution, 
    :d2_normal_distribution          => d2_normal_distribution
  )
end

#time_value ⇒ Object

Time Value The value of an option that captures the chance of further appreciation before expiration. The value of an option can be broken down into intrinsic value, or the value of the option if it were exercised today, and time value, or the added value of the option over and above the intrinsic value. For example, if a stock is trading at $40 and a call with a strike price of $35 were trading for $7, the call would have a $5 intrinsic value ($40-$35) and a $2 time value ($7-$5). Time value will decay by expiration assuming the underlying security stays at the same price.



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# File 'lib/greeks.rb', line 124

def time_value
  @time_value ||= GreekCalculations.time_value(
    :option_price  => option_price,
    :premium_value => premium_value
  )
end

#to_hash ⇒ Object 



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# File 'lib/greeks.rb', line 283

def to_hash
  hash = {
    :federal_reserve_interest_rate => federal_reserve_interest_rate,
    :stock_dividend_rate           => stock_dividend_rate,
    :stock_price                   => stock_price,
    :option_expires_in_days        => option_expires_in_days,
    :option_type                   => option_type,
    :option_strike                 => option_strike,
    :option_price                  => option_price,
    :iv                            => (NilMath.new(iv)         * 100.0).to_f,                      # iv * 100
    :delta                         => (NilMath.new(delta)      * stock_price / option_price).to_f, # delta * stock_price / option_price
    :gamma                         => (NilMath.new(gamma)      * stock_price / delta).to_f,        # gamma * stock_price / delta
    :vega                          => (NilMath.new(vega)       * 100.0 * iv / option_price).to_f,  # vega * iv * 100 / option_price
    :rho                           => (NilMath.new(rho)        * 100.0 / option_price).to_f,       # rho * 100 / option_price
    :theta                         => (NilMath.new(theta)      * 100.0 / option_price).to_f,       # theta * 100 / option_price
    :deta_vs_theta                 => nil,
    :break_even                    => (NilMath.new(break_even) * 100.0).to_f,                      # break_even * 100
  }

  # Delta/Theta
  # A measure of the “bang for the buck” of an option.
  # By dividing the dimensionless Delta or leverage of an option by the dimensionless Theta or 
  # decay rate, the trend in the Delta/Theta column indicates which options give the most exposure
  # to the movement of the underlying stock or index for a given decay rate of the option value.
  # The highest numbers indicate the most bang for the buck for the least decay rate.
  hash[:deta_vs_theta] = (NilMath.new(hash[:delta]) / hash[:theta]).to_f

  # Iterate the generated columns and round the output
  [:break_even, :iv, :delta, :gamma, :vega, :rho, :theta, :deta_vs_theta].each do |key|
    hash[key] &&= hash[key].round(2)
  end

  hash
end

#vega ⇒ Object

Vega The change in the price of an option for a change in the implied volatility of the option, all else held equal. In general, as the options market thinks it is more difficult to value a stock, implied volatility and therefore the price of the options will increase. For example, if an option is trading for $1, the implied volatility is 20%, and the vega is $0.05, then a one-percentage-point increase in implied volatility to 21% would correspond to an increase in the price of the option to $1.05. In percentage terms, the vega in this case would be ($0.05/$1.00)/(1 percentage point) = 5%.



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# File 'lib/greeks.rb', line 236

def vega
  @vega ||= GreekCalculations.vega(
    :price_vs_rate_vs_expires     => price_vs_rate_vs_expires, 
    :option_expires_pct_year_sqrt => option_expires_pct_year_sqrt,
    :nd1                          => nd1, 
    :iv                           => iv
  )
end