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Important groundwork for the numerical(i.e.,non-formula-based)valuation of options in practice was laid by Cox and Ross,who established the replication principle and risk-neutral valuation.The replicating principle stipulates that the payoff(and therefore,the value)of an option can be replicated from an equivalent portfolio of traded securities and cash.Risk-neutral valuation implies that the valuation of options is independent of the risk preferences of investors and thus,in a sense,universal.
Starting in 1976,alternative option pricing models were developed.They subsequently relaxed some of the stringent assumptions of the Black/Scholes model and thus contributed to a more realistic modeling of the option price.Cox and Ross developed the constant elasticity of variance model,which represents the volatility of the stock prices in a more realistic way.next to emerge were Merton's jump diffusion model and the pure jump model developed by Cox,Ross and Rubinstein,which allowed the stock price to follow a jump process instead of the purely continuous process assumed by Black/Scholes.Finally,Geske's compound option model and Rbuinstein's displaced diffusion model replaced the stock price as the underlying asset with different combinations of debt and the value of the firm.
Important groundwork for the numerical(i.e.,non-formula-based)valuation of options in practice was laid by Cox and Ross,who established the replication principle and risk-neutral valuation.The replicating principle stipulates that the payoff(and therefore,the value)of an option can be replicated from an equivalent portfolio of traded securities and cash.Risk-neutral valuation implies that the valuation of options is independent of the risk preferences of investors and thus,in a sense,universal.
Starting in 1976,alternative option pricing models were developed.They subsequently relaxed some of the stringent assumptions of the Black/Scholes model and thus contributed to a more realistic modeling of the option price.Cox and Ross developed the constant elasticity of variance model,which represents the volatility of the stock prices in a more realistic way.next to emerge were Merton's jump diffusion model and the pure jump model developed by Cox,Ross and Rubinstein,which allowed the stock price to follow a jump process instead of the purely continuous process assumed by Black/Scholes.Finally,Geske's compound option model and Rbuinstein's displaced diffusion model replaced the stock price as the underlying asset with different combinations of debt and the value of the firm.
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