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BLACK-SCHOLES OPTIONS PRICING MODEL

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					BLACK-SCHOLES OPTIONS
    PRICING MODEL
After completing the chapter,

1. you should be able to calculate the fair value of
   an option, and
2. decide whether the market price of the option
   is high or low than the fair value.




                     Overview of Management
     Intrinsic & Speculative Value
Intrinsic Value: Value of the option if it was
  to expire immediately.
  o IVc = max {Po - X, O}
  o IVp = max {X - Po, O}


Speculative Value: Value of the option
 minus the intrinsic value.
     Option Value – Intrinsic Value


                    Overview of Management
                       BSOPM
BSOPM depends on the five factors to
calculate the fair value of options. These
are:

   Stock Price (P0),
   Exercise (Strike) Price,
   Time to Expire (t) in years,
   Volatility (σ)
   Risk Free Rate (kRF)



                         Overview of Management
THE FORMULA UNDER BSOPM

 Vc = P0 Nd1 -      X Nd2
                   ekRFt

 d1 = ln (P0/X) + (kRF + 0.5 σ2)t
                σ√t

 d2 = d1 - σ√t

 Vp = V c +    X      - P0
              ekRFt




                             Overview of Management
               Example Vc
Given,
    Stock Price (P )0                      = $62
    Exercise Price (X)                     = $60
    Time to Expiration (t)                 = 40 days
    Volatility (σ)                         = 32%
    Risk Free Rate                         = 4%




                  Overview of Management
                                 Solution
Step I: To calculate, Value of Call (Vc), first we
need to calculate d1 and d2
         So
         d1 = ln P0/X + (kRF + 0.5 σ2)t
                      σ√t
         d1 = ln 62/60 + (0.04 + 0.5*0.322) * 40/365
                      0.32 √(40/365)
         d1 = 0.404

          d2 = d1 - σ√t
          d2 = 0.404 – 0.32√(40/365)

          d2 = 0.298

Accordingly, d1 = 0.40 and d2 = 0.30




                                       Overview of Management
                            Solution
Accordingly, d1 = 0.40 and d2 = 0.30

Step II: Find the value of d1 and d2 from the table showing
   ‘Cumulative Area under Standard Normal Distribution Table’

So,     Nd1 = 0.6554 and Nd2 = 0.6179

Step III: Put various values into the Vc formulae
         Vc = P0 Nd1 - X Nd2
                       ekRFt
          Vc = 62 * 0.6554 – (60/1.004389)* 0.6179
             = 40.6348 – 59.7378*0.6179
             = 40.6348 – 36.912
             = $3.72



                              Overview of Management
                       Solution Vp

Vc = P   0   Nd1 -     X     Nd2
                     ekRFt

d1 = ln P0/X + (kRF + 0.5 σ2)t
              σ√t

d2 = d1 - σ√t


Vp = Vc +        X      - P0
               ekRFt


                               Overview of Management
Thanks

 Overview of Management

				
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