On the Consistency of a Firm’s Value with a Lognormal Diffusion Process
Affiliation(s)
Department of Finance, Fairleigh Dickinson University, Vancouver, Canada. Department of Finance, Laval University, Quebec, Canada.
Department of Finance, Fairleigh Dickinson University, Vancouver, Canada. Department of Finance, Laval University, Quebec, Canada.
ABSTRACT
A partial equilibrium model is developed to examine conditions supporting the representation of the value of a firm by the lognormal diffusion process. The model formalizes the operating side of the firm and leads to a formula valuing the firm’s risky profit stream. The present value formula is then compared to the existing work on valuing exogenous risky income stream. Implications of the resulted pricing model on the volatility of the firm value processes are explored.
A partial equilibrium model is developed to examine conditions supporting the representation of the value of a firm by the lognormal diffusion process. The model formalizes the operating side of the firm and leads to a formula valuing the firm’s risky profit stream. The present value formula is then compared to the existing work on valuing exogenous risky income stream. Implications of the resulted pricing model on the volatility of the firm value processes are explored.
KEYWORDS
Cashflow Valuation; Adjustment Cost; Non-Constant Volatility Process; Lognormal Distribution
Cashflow Valuation; Adjustment Cost; Non-Constant Volatility Process; Lognormal Distribution
Cite this paper
A. Cheung and V. Lai, "On the Consistency of a Firm’s Value with a Lognormal Diffusion Process," Journal of Mathematical Finance, Vol. 2 No. 1, 2012, pp. 31-37. doi: 10.4236/jmf.2012.21003.
A. Cheung and V. Lai, "On the Consistency of a Firm’s Value with a Lognormal Diffusion Process," Journal of Mathematical Finance, Vol. 2 No. 1, 2012, pp. 31-37. doi: 10.4236/jmf.2012.21003.
References
[1] R. C. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, 1974, pp. 449-470. doi:10.2307/2978814 [2] M. Rubinstein, “The Valuation of Uncertain Income Streams and the Pricing of Options,” Bell Journal of Economics and Management Science, Vol. 7, 1976, pp. 407-425. [3] S. A. Ross, “A Simple Approach to the Valuation of Risky Streams,” Journal of Business, Vol. 51, No. 3, 1978, pp. 453-475. doi:10.1086/296008 [4] P. J. Schonbucher, “Credit Derivatives Pricing Models,” John Wiley and Sons, New York, 2003. [5] A. Bick, “On the Consistency of Black Scholes Model with a General Equilibrium Framework,” Journal of Financial and Quantitative Analysis, Vol. 22, No. 3, 1987, pp. 259- 275. doi:10.2307/2330962 [6] J. C. Hull and A. White, “The Pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance, Vol. 42, No. 2, 1987, pp. 218-300. doi:10.2307/2328253 [7] L. O. Scott, “Option Prices When the Variance Changes Randomly,” Journal of Financial and Quantitative Analysis, Vol. 22, No. 4, 1987, pp. 419-438. doi:10.2307/2330793 [8] S. Heston, “A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Cu- rrency Options,” Review of Financial Studies, Vol. 6, No. 2, 1993, pp. 327-345. doi:10.1093/rfs/6.2.327 [9] R. Goldberg, “Methods of Real Analysis,” John Wiley and Sons, New York, 1976.
[1] R. C. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, No. 2, 1974, pp. 449-470. doi:10.2307/2978814 [2] M. Rubinstein, “The Valuation of Uncertain Income Streams and the Pricing of Options,” Bell Journal of Economics and Management Science, Vol. 7, 1976, pp. 407-425. [3] S. A. Ross, “A Simple Approach to the Valuation of Risky Streams,” Journal of Business, Vol. 51, No. 3, 1978, pp. 453-475. doi:10.1086/296008 [4] P. J. Schonbucher, “Credit Derivatives Pricing Models,” John Wiley and Sons, New York, 2003. [5] A. Bick, “On the Consistency of Black Scholes Model with a General Equilibrium Framework,” Journal of Financial and Quantitative Analysis, Vol. 22, No. 3, 1987, pp. 259- 275. doi:10.2307/2330962 [6] J. C. Hull and A. White, “The Pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance, Vol. 42, No. 2, 1987, pp. 218-300. doi:10.2307/2328253 [7] L. O. Scott, “Option Prices When the Variance Changes Randomly,” Journal of Financial and Quantitative Analysis, Vol. 22, No. 4, 1987, pp. 419-438. doi:10.2307/2330793 [8] S. Heston, “A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Cu- rrency Options,” Review of Financial Studies, Vol. 6, No. 2, 1993, pp. 327-345. doi:10.1093/rfs/6.2.327 [9] R. Goldberg, “Methods of Real Analysis,” John Wiley and Sons, New York, 1976.