Understanding Call and Put Options Premiums in Finance Case Study

Question 1: Computation of the Premium for the call option and put option

“Put option” and “call option” are the two financial contracts that are specified on the underlying assets. These financial contracts can be present in the forms of stocks, currencies, and commodities as per suitability. Moreover, in the case of the call option, the holder has the statutory right to buy the stocks. On the contrary, the put option gives the right to the holder for selling the stocks (Guo and Lin, 2020). “Black Scholes Model” is one of the effective theories in the “modern financial theory”. This model helps to decide specific beliefs which can guide forecasts from the real-world result. Also, this model helps to calculate the exact price for the varieties of options contracts (Atta-Mensah, 2021). The numerical calculations help to evaluate how the financial statements will change in their cost values over the future. In this “Black Scholes Model,” there are some prices included, they are “the price of stock”, “the price of option strike”,” The rate of risk-free return” and also the volatility.

“The Black-Scholes model” works by reaching “a risky asset” to “a risk-free asset” such as “treasury bills”. Volitality of the asset is considered to be

Table 1: Computation of the Premium of Call Option and put option

C=SN (d1)−Ke−rtN (d2)

The above equation has been used in the above table to represent the premium of call and put option. Based on the above figure the stock price that has been identified is around £100 (SN). The strike prices are represented as D1=£ 180, D2=£100 respectively. The risk-free rate of the transactions is around 0.0077 (Ke). Thus, the intrinsic value that has been computed for the call option is near about £ 20 (rtN) and the premium for the call option is around £ 197.25. Moreover, the premium value for the K2 call option is assumed to be near £ 177.25 respectively. The D1 value of the put option is identified to be near about £ 20 and the premium value of the “put option” is near about £ 157.00. On the other hand, the intrinsic value of the D2 is near about 0 and the premium of the put option is around £ 177.00.

Different options are used for the strategies for the purpose of “call option” and “put option”

The various hedging strategies that are used for mitigating the risk and challenges of the call option and the put options are.

The consideration of the strike price and the expiration date are important to identify as the price of the higher strike prices will tend to reflect more costly for the seller owing to the high rate of risks attached to it (Li, 2019). Moreover, the higher price of the strike raising tends to create a protective layer on the price for the buyer.

Hedging is helping the investor to reduce the risk, which means it helps the investor to reduce the risk. This means it helps the investor at the time of a sudden fall in the price of the stock and the investor is holding the stock for the long period. In this situation, the investor will not suffer more losses. If the investor uses the hedging strategy properly then the investor does not suffer more loss at the time of price fall. a put option gives the right the investor to sell the stock at the time of the price fall. a call option is giving the right to buy the stock (Almeidaand Freire, 2022).
There is various option strategy rate available that help the investor at the time of trading. A covered& call is one of the strategies through which the investor can call. It is one of the famous strategies which most traders can use at the time of the trade, in which the trader can buy a naked call option. It is famous because in it there is minimum risk and a high degree of return or income (Baliet al. 2021). A married& put is one of the other strategies which most traders are used at the time of the trade. In which the investor buys a share, and after that, the investor continuously buys the put option. If the price of the stock is below the purchase price the trader will suffer a loss otherwise not.

“Hedging strategies” are mostly used by investors to decrease the value of risk according to a particular event in which the value of the assets suddenly falls down. “Hedging Strategies” are helps to decrease the value of loss without any changes on the values of “risk of return”. Company investors have the option to buy the put options from the protections which are on the downside (Zhang, 2021). If the investors are using “hedging strategies” then they are able to sell the stock at a selected cost within a provided time structure. Investors are usually better concerned with hedging against average price downhills than powerful declines, as these types of price decreases are both very surprising and fairly common. For these investors, a bear put space can be a “cost-effective hedging strategy”.

Question 2: Computation of the calculation for the “duration”,” modified duration”, and “convexity” with the help of the explanation

Table 2: Computation of the Duration, Modified Duration and Convexity

Table 3: Computation of the weightageon maturity

Based on the yield rate and the maturity of the bond, calculation of duration and modified duration is calculated. Changes in yield rate in the two months are acknowledged and duration is based on discounted cash flow. Whereas the coupon payment is based on the forest month yield rate, and the total value of cash flow and weighted cash flow is needed when calculating duration. However, the calculation of modified duration is totally based on the duration value. Besides, that convexity calculator needs weightage value and maturity weightage value. The value of convexity is the total value of the maturity weightage amount.

Question 3: Explanation of the benefits of the “Short hedger position” that improves in case of basic strengths unexpectedly and weakening

The concept of basis risk defines the difference between the assets which will be hedged and the spot price; along with that the future price of the contract is also included. However, the term strength refers to when the basis has an increased nature. Besides that, the decreasing nature of the basis refers to weakening. Accordingly, it is very beneficial for any hedger when the basis got strengthened as the price of any hedge assets got increases and the chances of earning money also got high. Along with that if any kind of weakening shows in the nature of the basis, then there will be a chance that the hedger can face loss in hedging (Carbonneau and Godin, 2021). As the value of assets got deceased deliberately and chances of earning money will also be decreased, therefore it can be said that the strength of the basis is more acceptable to the hedger, where the weakening arises the chances of low earnings.

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Discussion of the price values

The value of every commodity changes continuously, however, the changes in wheat price are the main factor here, which arises from the executive. The future value of each product can be determined based on the change in its value over the year. In this case, the executive thought that the use of wheat future is more expensive than using wheat in production. However, it is also assumed that in the future there will be a chance that the price of wheat will be less than the price of wheat future. Therefore, the executive offered to the treasures that it would be better if the company shifted from the wheat future to normal wheat. However, as a treasure, it is important to notice what will be more beneficial for the company. Accordingly, it is suggested that the company should prioritize the matter which is arisen by the executive, and take action according to that. Along with that the future price for both commodities should be knowledgeable by the company band take decisions based on that.

References

Almeida, C. and Freire, G., 2022. Pricing of index options in incomplete markets.& Journal of Financial Economics,& 144(1), pp.174-205.

Atta-Mensah, J., 2021. Commodity-linked bonds as an innovative financing instrument for African countries to build back better.& Quant. Financ. Econ,& 5, pp.516-541.

Bali, T.G., Beckmeyer, H., Moerke, M. and Weigert, F., 2021. Option return predictability with machine learning and big data.& Available at SSRN 3895984.

Carbonneau, A. and Godin, F., 2021. Equal risk pricing of derivatives with deep hedging. Quantitative Finance, 21(4), pp.593-608.

Guo, B. and Lin, H., 2020. Volatility and jump risk in option returns. Journal of Futures Markets, 40(11), pp.1767-1792.

Li, P., 2019. Pricing exotic option under stochastic volatility model.

Zhang, J., 2021. Dynamic index optimal investment strategy based on stochastic differential equations in financial market options.& Wireless Communications and Mobile Computing,& 2021.