Applications of option pricing in corporate

Types of real option[ edit ] Simple Examples Investment This simple example shows the relevance of the real option to delay investment and wait for further information, and is adapted from "Investment Example".

Applications of option pricing in corporate

There are Cablevision bonds, due inthat have been traded from toand the variance in ln monthly price s for these bonds is 0. The correlation between stock price and bond price changes has been 0.

The stock and bond price variance are first annualized: The parameters of equity as a call option are as follows: In most such investments, there is a cost associated with developing the resource, and the difference between the value of the asset extracted and the cost of the development is the profit to the owner of the resource.

Defining the cost of development as X, and the estimated value of the resource as V, the potential payoffs on a natural resource option can be written as follows: Time to Expiration Relinqushment Period: Time to exhaust inventory - based upon inventory and capacity output. Variance in value of underlying asset based upon variability of the price of the resources and variability of available reserves.

Development Lag Calculate present value of reserve based upon the lag. A gold mine Consider a gold mine with an estimated inventory of 1 million ounces, and a capacity output rate of 50, ounces per year.

The firm owns the rights to this mine for the next twenty years. The inputs to the model are as follows: It will take twenty years to empty the mine, and the firm owns the rights for twenty years. Every year of delay implies a loss of one year of production.

Valuing the Option Based upon these inputs, the Black-Scholes model provides the following value for the call: The additional value accrues directly from the mine's option characteristics. Inputs to the Black-Scholes Model Given this information, the inputs to the Black-Scholes can be estimated as follows: The estimated opportunity cost of this delay is the lost production revenue over the delay period.

Extending the option pricing approach to value natural resource firms Since the assets owned by a natural resource firm can be viewed primarily as options, the firm itself can be valued using option pricing theory. The preferred approach would be to consider each option separately, value it and cumulate the values of the options to get the value of the firm.

Since this information is likely to be difficult to obtain for large natural resource firms, such as oil companies, which own hundreds of such assets, a variant of this approach is to value the entire firm as one option.

A purist would probably disagree, arguing that valuing an option on a portfolio of assets as in this approach will provide a lower value than valuing a portfolio of options which is what the natural resource firm really own.

Applications of option pricing in corporate

Nevertheless, the value obtained from the model still provides an interesting perspective on the determinants of the value of natural resource firms. Inputs to the Black-Scholes Model Input to model Corresponding input for valuing natural resource firm Value of underlying asset Value of cumulated estimated reserves of the resource owned by the firm, discounted back at the dividend yield for the development lag.

Exercise Price Estimated cumulated cost of developing estimated reserves Time to expiration on option Average relinquishment period across all reserves owned by firm if known or estimate of when reserves will be exhausted, given current production rates.

Riskless rate Riskless rate corresponding to life of the option Variance in value of asset Variance in the price of the natural resource Dividend yield Estimated annual net production revenue as percentage of value of the reserve. The average relinquishment life of the reserves is 12 years.

The bond rate at the time of the analysis was 9. The variance in oil prices is 0. The present value of these developed reserves, discounted at the weighted average cost of capital of Valuing product patents as options The General Framework A product patent provides the firm with the right to develop the product and market it.

It will do so only if the present value of the expected cash flows from the product sales exceed the cost of development. If this does not occur, the firm can shelve the patent and not incur any further costs.

If I is the present value of the costs of developing the product, and V is the present value of the expected cashflows from development, the payoffs from owning a product patent can be written as: Variance in value of underlying asset Variance in cash flows of similar assets or firms Variance in present value from capital budgeting simulation.

Exercise Price on Option Option is exercised when investment is made. Cost of making investment on the project; assumed to be constant in present value dollars.Advanced Security Solutions and Options for SaaS, PaaS, and IaaS Customers to Help Accelerate Your Response to GDPR.

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Option pricing when underlying stock returns are discontinuous - ScienceDirect