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David Goldenberg
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It is not possible to accurately forecast demand, supply or price of commodities far into the future.
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dSt=mStdt + sStdZt
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this is typically the most difficult part of calculating any option price
historical volatility of same or similar assets is usedSD t=Tt.wis the time to expiration
given R&D spending in 2002 $ and commercialization in 2050
time to expiration is 48 years
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cost of building and decommissioning nuclear fusion facilities to meet demands for first fifty years of commercialization
note this involves all fixed costs XZZ8ZZZWHExample Under Consideration48 billion US 2002$ R&D Required
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0.4% adoption rate per year of global energy consumption
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Jonathan Linton
Desmarais Chair in the Management of Technological Enterprises
School of Management
University of Ottawa
Ottawa, On
David Goldenberg
Rensselaer Polytechnic Institute
Troy, NY@P u * XII:!Application of Capital Budgeting "!$o Need to assume that costs and revenues are known in the future.
It is not possible to accurately forecast demand, supply or price of commodities far into the future.
It is not possible to forecast the degree of success of an R&D program in the future or the rate of improvement in technology in the future.
Attempts to do so are needed, but easily challenged."pZkYJAn Alternative Approach
J<Simplest Case BlackScholes $N(.) is the standard cumulative normal distribution.
St is the current stock price,
r is the annualized riskfree rate,
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t=Tt is the time to expiration, and
E is the exercise price.
fZ6CW?K;0Assumptions of the BlackScholes Pricing Formula11$ The model assumes that the underlying asset follows a stationary lognormal diffusion process described by the stochastic differential equation:
dSt=mStdt + sStdZt
where Zt is a standard arithmetic Brownian Motion process.
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Black, Scholes, and Merton won the Nobel prize in economics for this model in 1997 under the title for a new method to determine the value of derivatives .
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no assumptions required
D/JPA St is the current stock price
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.9RQB rXis the annualized riskfree rate
we utilize the average annualized Treasury Bill yield..!7YRC s is the annualized instantaneous volatility of percentage rates of return on the stock
this is typically the most difficult part of calculating any option price
historical volatility of same or similar assets is usedSD t=Tt.wis the time to expiration
given R&D spending in 2002 $ and commercialization in 2050
time to expiration is 48 years
P;xTE Eis the exercise price
the exercise price is the cost of obtaining the benefit
cost of building and decommissioning nuclear fusion facilities to meet demands for first fifty years of commercialization
note this involves all fixed costs XZZ8ZZZWH4Assessment of Needed Benefits to Make R&D worthwhile55UF!Additional notes on BlackScholes""If the stock price, the expected savings, is desirable than the R&D should be conducted
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Jonathan Linton
Desmarais Chair in the Management of Technological Enterprises
School of Management
University of Ottawa
Ottawa, On
David Goldenberg
Rensselaer Polytechnic Institute
Troy, NY@P u * XII:!Application of Capital Budgeting "!$o Need to assume that costs and revenues are known in the future.
It is not possible to accurately forecast demand, supply or price of commodities far into the future.
It is not possible to forecast the degree of success of an R&D program in the future or the rate of improvement in technology in the future.
Attempts to do so are needed, but easily challenged."pZkYJAn Alternative Approach
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St is the current stock price,
r is the annualized riskfree rate,
s is the annualized instantaneous volatility of percentage rates of return on the stock,
t=Tt is the time to expiration, and
E is the exercise price.
fZ6CW?K;0Assumptions of the BlackScholes Pricing Formula11$ The model assumes that the underlying asset follows a stationary lognormal diffusion process described by the stochastic differential equation:
dSt=mStdt + sStdZt
where Zt is a standard arithmetic Brownian Motion process.
PPGP9 L=Assumptions (cont.)$ Under this description the lognormal diffusion process is essentially Geometric Brownian Motion.
Black, Scholes, and Merton won the Nobel prize in economics for this model in 1997 under the title for a new method to determine the value of derivatives .
DZZ(
O@ N(.) J
is the standard cumulative normal distribution
no assumptions required
D/JPA St is the current stock price
not available for real assets
Consequently, we calculate the real stock price that makes the option attractive
.9RQB rXis the annualized riskfree rate
we utilize the average annualized Treasury Bill yield..!7YRC s is the annualized instantaneous volatility of percentage rates of return on the stock
this is typically the most difficult part of calculating any option price
historical volatility of same or similar assets is usedSD t=Tt.wis the time to expiration
given R&D spending in 2002 $ and commercialization in 2050
time to expiration is 48 years
P;xTE Eis the exercise price
the exercise price is the cost of obtaining the benefit
cost of building and decommissioning nuclear fusion facilities to meet demands for first fifty years of commercialization
note this involves all fixed costs XZZ8ZZZWHBlackScholes Get stuff from the Options Paper!!UFMaxmin CalculationsIf the stock price, the expected savings, is desirable than the R&D should be conducted.
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Jonathan Linton
Desmarais Chair in the Management of Technological Enterprises
School of Management
University of Ottawa
Ottawa, On
David Goldenberg
Rensselaer Polytechnic Institute
Troy, NY@P u * XII:!Application of Capital Budgeting "!$o Need to assume that costs and revenues are known in the future.
It is not possible to accurately forecast demand, supply or price of commodities far into the future.
It is not possible to forecast the degree of success of an R&D program in the future or the rate of improvement in technology in the future.
Attempts to do so are needed, but easily challenged."pZkYJAn Alternative Approach
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St is the current stock price,
r is the annualized riskfree rate,
s is the annualized instantaneous volatility of percentage rates of return on the stock,
t=Tt is the time to expiration, and
E is the exercise price.
fZ6CW?K;0Assumptions of the BlackScholes Pricing Formula11$ The model assumes that the underlying asset follows a stationary lognormal diffusion process described by the stochastic differential equation:
dSt=mStdt + sStdZt
where Zt is a standard arithmetic Brownian Motion process.
PPGP9 \M
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Black, Scholes, and Merton won the Nobel prize in economics for this model in 1997 under the title for a new method to determine the value of derivatives .
DZZ(
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is the standard cumulative normal distribution
no assumptions required
D/JPA St is the current stock price
not available for real assets
Consequently, we calculate the real stock price that makes the option attractive
.9RQB rXis the annualized riskfree rate
we utilize the average annualized Treasury Bill yield..!7YRC s is the annualized instantaneous volatility of percentage rates of return on the stock
this is typically the most difficult part of calculating any option price
historical volatility of same or similar assets is usedSD t=Tt.wis the time to expiration
given R&D spending in 2002 $ and commercialization in 2050
time to expiration is 48 years
P;xTE Eis the exercise price
the exercise price is the cost of obtaining the benefit
cost of building and decommissioning nuclear fusion facilities to meet demands for first fifty years of commercialization
note this involves all fixed costs XZZ8ZZZWH4Assessment of Needed Benefits to Make R&D worthwhile55UF!Additional notes on BlackScholes""If the stock price, the expected savings, is desirable then the R&D should be conducted
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