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Unformatted text preview: Session 14: The Black Scholes Option Pricing Model A.
time to annualised current CCR annualised BS BS expiry days to expiry strike on risk stock call put price
Date option stock 8/07/04 option
date option in years price free asset std dev price price S T C P 30.75 26/08/04 expiry t 49 0.1342 X σ r
28 5.4159% d1 N(d1) d2 N(d2) 0.1068 2.5996 0.9953 2.5605 0.9948 2.9546 0.0017837289 B.
i) The probability of seeing the Aug 04 $28.00 NAB call option finishing out of the
money
= 1 – the probability that the option finishing in of the money
= 1 – N(d2) = 1 – 0.9948 = 0.0052.
ii) N(d1) or 0.9953 units of share are required.
iii)The amount is the expected present value of the exercise price
= XertN(d2)
= 28 × e5.4159% × 0.1342 × 0.9948 = $27.65.
iv) Intrinsic value = max{0, S  X} = {0, 30.75 – 28} = $2.75.
Time value = C – intrinsic value = 2.9546 – 2.75 = 0.2046.
C.
i) The larger the stock price, the larger is the call value and the smaller is the put value. A
larger S increases (reduces) the intrinsic value of the call (put), which is defined as
max{0, S – X} (max{0, X – S}).
ii) The longer the time to expiration, the larger are the call and put values. A longer t
raises the time value by increasing the probability of the option finishing in the money.
iii)The larger the exercise price, the smaller is the call value and the larger is the put value.
A larger X reduces (increases) the intrinsic value of the call (put).
iv) The larger the risk free rate, the larger the call value and the smaller the put value. A
larger r reduces the expected present value of the exercise price that we need to set aside
for potential exercise of the option, leaving us spare money to spend now. On the other
hand, a larger r reduces the expected present value of the exercise price that we can
borrow, leaving us less to spend now.
v) The larger the stock volatility, the larger are the call and put values. A larger σ raises
the time value by increasing the probability of the option finishing in the money.
D. N(x) is the area to the left of x under the unit normal distribution curve. It is the
probability of observing a value that is equal to or less than x.
E. It is because the total area under the unit normal distribution curve is 1 unit and
the distribution is symmetrical on either side of the mean at 0. 1 F.
i) BS model price = 35*0.8631 – 30e(0.047294*0.5)*0.8205
= 30.2085 – 24.0398
= 6.1687
Since the market price is $8.00, the call is overvalued.
ii) Since the call is overpriced,
• short or write a call
• buy N(d1) or 0.8631 shares
• borrow XertN(d2) or $24.0398
iii) Profit (in today’s $) made per call:
= $8 – 6.1687 = $1.8313 2 ...
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This note was uploaded on 10/23/2011 for the course FINS 2624 taught by Professor Hneryyip during the Three '10 term at University of New South Wales.
 Three '10
 HneryYip

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