Most of the underlying assets base their securities by determining its Derivatives. This concept implies that the change in the price of asset results to a change in the derivative thus making the price to be an underlying asset. Derivatives like options, swaps and futures offer a purpose for security which offers the manufacturers and producers a hedge risk opportunity. When two or more parties agree to use a derivative, a price is agreed on which would be applied later. The documentation of derivatives defines the relationship between the derivative and the underlying asset and trade conducted in a given market. As discussed below, it’s important to comprehend the full potential, the strength and the weakness of each derivative outlined
Types of Derivatives
Futures
Futures are a medium of exchange in an organised way determined by price, size and time of delivery of a product. An exchange standardises futures making it easier to trade. In every product used in exchange, the minimum set requirements must be set. Also, the size has a great impact on contract since it determines the units for trading in every contract provided. And the time of delivery gives the deadline to which the product should be available for a certain partnership. Standardization has helped manufacturers and producers access all the raw materials they require ( Strong & Jeyasreedharan, 2017) . Additionally, manufacturers can purchase several materials in exchange terms thus reducing hustle on multiple suppliers they acquire In the speculative mode, futures can be used when a company purchases assets by anticipating what the future holds: If the assets will appreciate or depreciate. It is mainly used by investors to determine if assets purchased can generate profit or loss ( McDonald, 2016) . In hedging mode, features are used to reduce the risk of adverse price fluctuation in assets.
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Options
Options are systems of derivatives, which deny a holder the commitment to buy or sell an underlying product at their price in the future. When obtaining an option to buy a commodity, it is termed as a “call”, and when one obtains the right to sell the same product, it’s known as a “put.” For one to know if the product is profitable, it important to determine the spot price and the strike price and then compare the two prices ( Strong & Jeyasreedharan, 2017) . After analysing this option a conclusion whether the product should sell or let to expire is determined. Also, when exercising these options, a business can find itself in three positions they can exercise. The first position is in the money (ITM); it’s when the option price it’s fairer than the spot price thus a more favourable exercise option ( Wilmott & Orrell, 2017) . The second position is the ATM (at the money) is more applicable when the spot price is equal to the strike price thus nothing is gain in the process. The last position is the OTM (over the money) it’s a position where the spot price is lower than the strike price. In when in this position, it’s better to leave the option to expire and later by the products at the current price on the market. Likewise there are two ways to settle options placed between the two parties; first, when exercising the option, it’s vital to pay the option holder upon the utilisation of the option. It’s more advantageous to have an option than a derivative. The advantage of an option is that option is not binding and does not require a person to buy a product. It gives one a right to buy or not to buy, but the option’s price is quite high then the market current price thus one can let the option expire an buy the product at a market price. The sole loss incurred by a person is the premium cost which maintains the option hence being able to buy at spot price ( Wilmott & Orrell, 2017) . Also, the option can be used as a hedging tool. This tool offers a successful investment risk for small businesses. In a speculative mode, options can be used to determine the speculative price of a property in the future. The speculative mode determines for the holder when it is appropriate to sell or buy property(McDonald, 2016). In hedging mode, options help the holder reduces risks that involve cashing out an asset since it provides the holder with the right but not obligation to buy or sell the property.
Swaps.
A swap is an exchange of cash flow between two parties under an agreement on a multiple and predetermined dates. A fixed rate agreed by two parties is paid by one while the other float rate is paid by the other party. For example, in a trading product the first party an airline company depends on kerosene pays a fixed predetermined price of the product while the second part a bank agrees to pay the sports fee for the product as float price. This concept ensures that the airline pays a fixed price agreed while the extra costs should be handled by the bank. And if the price fall beneath the fixed price agreed, the bank should be paid the difference fall in price. In the speculative mode, Swaps is used to cover for the future since it has a lot of uncertainties. Swaps cater for commodities or service despite its prices fluctuating(McDonald, 2016). However, in hedging mode, swaps reduce the risks involved in the pricing of commodities since the fluctuations of prices are insured.
Six inputs of Black-Scholes Option Pricing Model.
Underlying price
Underlying price is a given price at which the trading occurs at that particular moment known as option pricing. Using an example of J.P Morgan stock; the price at which the stocking is trading (option price) is the same price one will use as the underlying price. Delta concept is important in this input since it informs a person on the rise and fall of stock option thus getting profits when acquiring underlying option stock. If there is an increase in the underlying price increase, the caller will be affected since they will not be able to buy the stock because of its high price ( Strong & Jeyasreedharan, 2017) . However, if underlying price reduces the put will be able to attract many people to buy the stock.
Strike price
Strike price , also called exercise price, is the price at which you would buy (or sell) the underlying security if you choose to exercise the call (or put) option. It is one of the fixed specifications of each particular option contract, and it does not change during the life of the option. When the strike price increases then many people will not be able to exercise their call obligation since the stock price will be high. Whereas, if strike price decreases, then put option will be exercised since many people will be able to meet the strike price ( Strong & Jeyasreedharan, 2017) .
Time to expiration
Time to expiration is the period between which the option expires and the time of pricing of products. For example, the strike price, present individual option and the date it expires. Also, the date of expiry remains the same during the option period but as the time passes the option is left to expire. This way, the expiration of option is calculated in annually per percent, this calculation is obtained by software that allows you to input your current date and the date of expiry then it converts your information into percentage per annum spontaneously. Also, this calculation can be done on trading days/ calendar years if the time of expiration is increased then many people will be able to exercise the call option since they will have time to obtain money to buy the stocks. However, if time expiration decreases then the put option will be exercised fully since fewer stocks would be sold out.
Volatility
The volatility input is quantified in percentage every year. Similarly, it’s the expected underlying security to which option works. Deviation of standard returns is a new option for pricing thus proving to be a different concept with complications in number representation. Vega concept is important in this input since it determines option price. Volatility is quite cheaper than option price. So, depending on each pricing; when one goes up, the other goes too and the other way ( Wilmott & Orrell, 2017) . If volatility option is increased then the volatility of the stock become cheaper, and the call option is exercised fully compared to when the volatility is low.
Risk-free interest rate
Similar to volatility, free risks rate and interests are measured in percentage yearly. In a trader perspective; it’s the ability to deposit and borrow cash during the option period. When there is a low-interest rate the interest rate input lacks essence, but the interest rate input can gain importance if the interest rates are very high. Like volatility, the risk-free interest rate is also measured in percent per year ( Wilmott & Orrell, 2017) . Gamma is a concept is important in this input in Risk-free interest rate since it measures the progress of underlying stock given an exposure of option delta.
Dividend Yield
Dividend yield was not considered as inputs originally when in their Black-Scholes model version which was compiled as an expansion. In this setup, one can tell more about the dividend treatment in the version of Black-Scholes model in respect to papers by Merton, Scholes, and Black ( Wilmott & Orrell, 2017) . If the dividend yield of a stock is high, then the change of exercising the call option is high compared when the dividend yield is low.
Black-Scholes option pricing model and the Binominal Option
Black-Scholes option pricing model essentially calculates the theoretical value of European-style option while employing options like anticipated volatility, expiry time, anticipated dividend, and usual interest rate. On the other hand, an iterative procedure uses binomial option as a pricing criterion paving the way for points in timing, allowing for specifications and creation of time span which provides valuation date and states on the time of expiration of the option. These models lower the probability of prices to change and arbitrage removal.
Difference
Regarding the Black-Scholes
In 1973 the Black-Scholes-Merton formed a generic version. The version includes a successive extension to carter for dividends which are mostly incorporated with a reduced stock price which is the same as the present value of the required dividend stream ( Wilmott & Orrell, 2017) . Also, the generic version takes up six inputs which include; expected dividend yield, option term, stock, s riskless rate and expected volatility.
Regarding the binomial,
The Cox, Ross and Rubinstein (CRR) is a generic version of binomial which is named after the inventors. Similar to the Black-Scholes-Merton, the generic binomial uses volatility inputs to come out with two computation which is the magnitude of an up-jump and probability of an up-jump.
Since binomial uses numerical approach, it has endless variations which are endless, and one can assume its design ( Wilmott & Orrell, 2017) . The design includes the tree nodes which have three or more branches hence trinomial.
The Critical Inputs to Valuing Futures and Swaps.
Futures
Volatility : Volatility is a statistical measure of the distribution of returns for a specified security or market index. Volatility can either be measured by using the variance or the standard deviation between returns from that market index or equivalent security. Usually, the higher the volatility, the perilous the security ( Strong & Jeyasreedharan, 2017) .
Swaps
Coupon : A coupon is the yearly interest rate remunerated on a bond, it is expressed as a percentage of the face value.
A fixed-rate payment : A fixed-rate payment is an amount due each period by a borrower to a creditor under a fixed-rate loan ( Wilmott & Orrell, 2017) . The fixed-rate loan payments will be equal amounts until the loan plus interest are paid in full.
References
McDonald, R. (2016). Option Pricing Functions to Accompany Derivatives Markets.
Shahmoradi, A. (2016). Valuation of Crude Oil Futures, Options and Variance Swaps (Doctoral dissertation, University of Calgary).
Strong, R. A., & Jeyasreedharan, N. (2017). Understanding Derivatives: Options, Futures, Swaps, MBSs, CDOs and Others.
Wilmott, P., & Orrell, D. (2017). Deriving Derivatives. The Money Formula: Dodgy Finance, Pseudo-Science, and How Mathematicians Took Over the Markets , 83-107.
