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Ken Shah
FINC 580
Corning Option Valuation Steps:
1. Value Straight Bond
2. Valuing Conversion Option:
Forecast up/down stock price using binomial model
Forecast payoffs
Use standard binomial valuation to value the call option (see handout)
Obtain value of St. bond + conversion option value (per share – i.e. divide by # of shares in
conversion) over the entire tree
3. Valuing Callable Feature:
Forecast Bond price per period (to year 15) using the 2% yield. Price path over 15 years will
grow by 2% every year.
To the company, the value to calling (redeeming) bonds is:
Value = Max[Stock price per share, redemption bond price per share]
Therefore payoffs to calling (redeeming) are:
Payoff = Max[Bond+Convert. Option - Redemption value, 0]
Use binomial formula to value redemption option using payoffs above
Obtain value of: Bond + conversion option – Redemption option
4. Repuchase Option:
Assume that option is never exercised early
Calculate the strike price per share = strike price at year 10 / # of shares
Payoff = Max[Strike price per share – Bond value without repurchase option, 0]
Use binomial model to value this option payoffs
Alternatively, do the same assuming option is exercised early, and project payoffs upto year 5
only using exercise price in year 5. Repeat the binomial valuation.
Seattle University – ASBE
KEN SHAH
FINC 580
Binomial Model:
Need the following inputs:
o Risk free rate per period
o Path of underlying security values
Charting the path of security value:
If a security (e.g. underlying stock)
o has an annual standard deviation of σ per year
o and follows a binomial distribution (i.e., it can take 2 values next period)
then the two values next period are:
Up Value
SU  S  e
Down Value
h
S D  S  e
h
Where
S = current security value
h = length of period in years (e.g., if period = 6 months, h = .5)
σ= annual standard deviation of stock returns
For example, a stock has a current value of $100, and an annual standard deviation of
returns of 20%, and h = 1 (period is 1 year) then
SU = 100 x e.2 = $122.14
$122.14
$100
SD = 100 x e-.2 = $81.87
$81.87
From this stock value paths we can obtain the call option payoff path
Payoff = Max [S – X, 0]
Where
S = current security value
X = exercise price
Suppose the X = 100 in the above example then the two payoffs next period are
PU = Max [122.14 – 100, 0] = 22.14
PD = Max [81.87-100, 0 ] = 0
Now we can apply the binomial pricing formula for this one-period option:
Binomial Option Pricing Formula for a Call
Definitions:
Up factor
u  e
Down factor
h
d  e
h
Call Value:
Ce
 r f h
 q  PU   1  q   PD 
Where
q
e
r f h
d
ud
Note again:
C = value of call option
e = the napiers base (exponent)
PU = call payoff when security is ‘up’
PD = call payoff when security is ‘down’
h = length of period in years
rf = annual risk free rate
u = up factor defined above
d = down factor defined above
In the numerical example
PU = 22.14
PD = 0
h=1
rf = .05 (assume)
u = e^.2 = 1.2214
d = e^-.2 = 0.8187
Therefore,
e.051  .8187
 = 0.5775
q= q
1.2214  .8187
C  e .051  .5775  22.14  1  .5775  0 = $12.16
You can easily extend this model to multiple periods. Just work backwards from the last
period at each node.
Extending above example to two periods:
0
Stock
Price
1
2
149.18
0
100
C
122.14
100
Call
Payoff
1
2
49.18
22.14
81.87
0
0
67.03
0
First find the two call values C11 and C12. Then using C11and C12, find C
0
Call Value
1
2
C11 = 27.02
C = 14.84
C12 = 0
This method can be extended to any number of periods.
Note- Original Issue Discount
Assume a $100,000 three-year non-interest bearing note is purchased on January 1, 2000
for $86,384 (yielding an effective interest rate of 5%. Interest income is computed as
follows:
Year
Jan 1 Carrying Value
2000
2001
2002
86,384
90,703
95,238
+
Interest Income
4,319 (=86,384 x .05)
4,319 (=90,703 x .05)
4,319 (=95,238 x .05)
=
Dec. 31 Carrying
Value
90,703
95,238
100,000