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Lattice method example11/23/2023 ![]() As mentioned previously, a lattice model would simulate exercise behavior over the entire contractual term, rather than simply using the single average expected term as illustrated in Figure SC 8-7. One method to incorporate early-exercise behavior assumes exercises based on stock price appreciation. This wider range would result in a higher fair value for the option, because option value is derived only from the upside potential for stock price appreciation. If the volatility was assumed to be 50%, the range of possible stock prices at t 3 would be from $490 to $24. For example, at time t 3 (the vesting date) the stock prices are assumed to be within a range from $269 to $44 based largely on the 30% volatility assumption. The size of the range is driven primarily by the volatility assumption, although risk-free interest rates may also influence these values in some versions of the lattice model. ![]() For basic tree-diagrams such as those presented in Figure SC 8-6, Figure SC 8-7, Figure SC 8-8, Figure SC 8-9, and Figure SC 8-10, the model simplifies reality by assuming the stock price must fall within a given range. Had the tree-diagram been drawn with more nodes (e.g., monthly or daily prices), these finite price points would resemble a smooth probability distribution. In Figure SC 8-6, the binary forks in the tree-diagram determine the assumed annual prices to which the stock can move. Post-vesting termination rate – the likelihood that an employee will be compelled to make an exercise decision prior to the conclusion of the option's contractual term.Early exercise refers to the exercise of an option prior to the end of the contractual term. It is described as the expected ratio of stock price to exercise price at the time of exercise. Exercise multiple – also known as the suboptimal exercise factor, the exercise multiple is an assumption about "early exercise" behavior or patterns based on stock-price appreciation rather than the time that has elapsed since the grant date.Vesting period – the shortest period until the option can be exercised.Contractual term of the option – the maximum period for which the option can be held. ![]() A simple lattice model might incorporate an array of values for each of the four inputs related to employee exercise behavior: The Black-Scholes model reduces all possible employee exercise patterns to a weighted-average that is used as a single input-the expected term-while lattice models can incorporate a range of inputs describing possible exercise behavior. In a similar manner, lattice models can incorporate far more detailed assumptions about employees' future exercise patterns than the Black-Scholes model. Transfers and servicing of financial assets Revenue from contracts with customers (ASC 606) Loans and investments (post ASU 2016-13 and ASC 326) Investments in debt and equity securities (pre ASU 2016-13) Insurance contracts for insurance entities (pre ASU 2018-12) ![]() Insurance contracts for insurance entities (post ASU 2018-12) IFRS and US GAAP: Similarities and differences Business combinations and noncontrolling interestsĮquity method investments and joint ventures
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