The advanced practice nurse is updating the plan of care of nursing home patients with hypertension.
Briefly describe the therapeutic actions of drugs affecting blood pressure (diuretics, ACE inhibitors, ARBs, CCB, sympathetic nervous system drugs).
What important teaching points should be addressed for patients receiving antihypertensive drugs?
Barone Adesi and Whaley (1987) developed a method to approximate analytically and easily the price of American options. They considered that the American and European option pricing equation is represented by the partial differential equation (3.2.1) developed by Black and Scholes (1987) and Merton (1987), (3.2.1) Barone Adesi and Whaley (1987) assumed that if this is true, then the early exercise premium of the American option, which is the price difference between the American and the European call option prices (3.2.2), can be represented by the same partial differential equation (3.2.3). (3.2.2) (3.2.3) The above equation after some transformation, shown on Barone Adesi and Whaley (1987) paper, and applying an approximation of a term tending to zero, yields the following quadratic equation, (3.2.4) Where (3.2.5), (3.2.6) and (3.2.7). Equation (3.2.4) “is a second order ordinary differential equation with two linearly independent solutions of the form . They can be found by substituting (3.2.8) into” equation (3.2.4) Barone Adesi and Whaley (1987), (3.2.9) With a general solution of the form, (3.2.10) When the American option boundary conditions are applied to the above solution and considering , then must be equal to 0 as when the asset price tends to zero so does the option price, resulting in the following American call option pricing equation, Barone Adesi and Whaley (1987), (3.2.11) From (3.2.9) we have the value for so the only value missing is . This can be calculated interactively considering another boundary condition of American call options. We know that in early exercise the payoff will never be higher than S – X, so from a critical underlying asset value the option payoff curve must be tangent to the S – X curve, which means that below the critical asset value the pricing equation is represented by (3.2.11), Barone Adesi and Whaley (1987). The algorithm presented by Barone Adesi and Whaley (1987) for the above pricing problem is presented further in the paper in the section dedicated to the implementation of the American option pricing models. 3.3 Lattice Methods Cox, Ross and Rubinstein (1979) proposed a model where the underlying asset would go up or down from one time step to the next by a certain proportional amount and with a certain probability until maturity. Due to the up and down characteristic of the asset price model these type of models are characterised by a binomial tree or, in the cases of the existence of a third possible movement, they are characterised by a trinomial tree, therefore named as Binomial or Trinomial models The price of the option would be recursively derived from maturity, due to the boundary condition as has been referenced before that the price of the option is only known with certainty at maturity. This means that the price of the option is calculated at maturity and recursively at each node up to the initial value, by discounting backwards at the risk free rate and respective probabilities. Due to the characteristic of American options, the model has to check if it is optimal to exercise the option at each node or if it has the advantage to continue to the next one, for example on the case of dividend payments. In the case that it is optimal to exercise the option at a certain node, its price will be equal to the intrinsic value at that same node. Every node will be checked for the optimality of exercising the option or not, until we have reached the initial point where we want to price the option. 3.3.1 Binomial Tree Model The model starts being built for a American option of a non dividend paying stock and after that the scenario of dividend payments and optimal early exercise strategy is considered. As referenced before the stock goes up and down by a certain amount form one period to the next, if u is the up movement and d the down movement, then they can be calculated as, (188.8.131.52) and (184.108.40.206) as in Cox, Ross and Rubinstein (1979). In no arbitrage conditions it is possible to calculate the probability of the up and down movements, with the up being defined as, (220.127.116.11) where f>GET ANSWER