Option Pricing Assignment

Q.1. Applying Black scholes option pricing model with the inclusion of the underlying parameters

S = current stock price(opening price)

T = time to maturity

K= strike price

S = volatility with greek letter or character sigma

q = dividend rate

where So = underlying price

X = Strike price (fixed price) =1170

Sigma = volatility

R = Continuously compounded risk – free interest rate

q = Continuously compounded dividend yield

t = time of expiration

where t = 30days (% of year) = 30/100x 360 = 108 choice implied volatility = 0.33939

3 month whereby, 90/100 x 360 = 324

324 – 108 = 216/100 = 2.16%

Closing price = 1200 – 1170 = $30

(1aii) when the price is compared to the midpoint value of ask price 41.5$, the resulting difference of 11.5$

(1b) we cannot find dividend yield when there are no observable difference between the ask price and the black scholes model option price This gives rise to a state of indecisive and indeterminate exercise and therefore initiate an outstanding and impeccable rise to run activity. This in no doubt lives us with a risk free investment.

Q2.

2a. plot

The graph which showed slight variation in volatility as against option pricing model where happens to have large marginal volatility, basically the price option to volatility plot shows close features. Furthermore, the feasibility of the plot owns it performance only to these two parameters which might not be firm in the option pricing model. Which gives an exact sensitivity value of one Option pricing model therefore inundates a reference point with a grip to the plot showing that the plot has certain deviation features as it cut across the two variable parameters and at every point of the deviation becomes bounded and surrounded by a fall

2b. plot

2b. Option price also experiences certain deviation as much as time to maturity as there is a geometrical increase in price with increase in time of maturity . When this observable change or changes is compared to option pricing model, the reverse is always the case. Which leaves a sensitivity value less than one. An option’s price depends on how long it has to run to expiration. Constructively and Intuitively, the longer the time to expiry, the higher the likelihood that it will end up in-the-money. Hence, longer dated options tend to have higher values, regardless of whether they are puts or calls. The time value subsequently decays to 0 as it nears expiry.

2c plot

The option price shows a decline with interest rate making the sensitivity less than one as compared with the option price model which turnouts to give a sensitivity value slightly greater but close to one than the value obtained from BSM. However, the interest rates effect an impact on option value through the option pricing model with use as a discount rate. Constructively and Intuitively, calls imply getting the upside of holding the underlying shares without dishing out the full price. Because a call buyer doesn’t need to purchase the full price of the stock, the difference between the full stock price and the call option could theoretically be invested and therefore, the call option should have a higher value for higher discount rates. The sensitivity to interest rates is measured by Rho, with higher interest rates increasing the value of calls and vice-versa for puts.

Q3.From the plot . it is experiences no optimal outcome and this is as a result of the variation in the volatility value which in no doubt act in declination with respect to other imperative parameters. The option pricing model facilitates the need to run a marginal appraisal of the key parameters which negate the outlook and outcome of a BSM quality.

Option pricing model Viz a vis the core parameters which indicate the unhealthy performances of the commercial venture solvency characteristics and marginalization owns it attributes to decline in calls and puts values with prompt reversal on this trend .

Q4.From the plot, it is imperative to invest early as there also might occur a decline in solvency, therefore making the early exercise to fall drastically beyond normal. As against the option pricing where the need for early exercise is not as important as BSM making it suitable for this option.

In a option pricing scenario and in a long-run it so much works for long term dealings and which conversely eradicates instability within a stipulated or confined area of the plot , herein a pictorial representation of the performances of the said parameters. The longer the state of investment , the healthier the investment and vice versa with option pricing functionalities

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