Derivatives

Forwards and Futures play an extremely important role in the current world of finance and investment. Long-term investors, speculators, and hedgers extensively use them. They enable market participants to establish large positions with smaller market impacts and lower transaction costs. Many Forward and Future contracts are in fact much more liquid than the underlying securities, and sometimes trade a larger volume than the underlying markets.

In this course – Forwards and Futures, the basic financial theories and concepts relevant to the topic will be discussed. The relationship between Forwards and Futures and the underlying security will also be explained. We'll also review concepts such as cost of carry, transportation, storage, and convenience factors that should be incorporated in the valuation of Forwards and Futures.

This course also looks into the application of Forwards and Futures in equity, commodity, and interest rate markets. The importance of margin in Future trading, type of contracts, and their specifications such as size, maturity, and pricing standards are also explored.

Forwards and Futures are important hedging tools used by individuals as well as institutions and companies. Therefore, it is important to examine the concept of hedging and the role of Forwards and Futures.

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In this course, three methods are presented for pricing an option.

1. 1. The first method is an analytical one whereby the Black Scholes formula is used to price a call or a put. The drawback of the analytical approach is that it only works for European options.
2. 1. The second method presented is the binomial tree, which is illustrated in the pricing of an American option to facilitate early exercise.
3. 1. The third method presented is the Monte Carlo simulation.

Then the assumption of constant volatility is challenged, due to the presence of the volatility smile, which is formally defined and shown to be empirically observed in all derivatives markets. Monte Carlo simulations are run to generate a distribution with kurtosis -- a mixture of normal distributions.

Finally, the Heston Model, which relaxes the assumption of constant volatility is presented.

• • • First, the Heston Model is shown to incorporate kurtosis by allowing volatility.
• • Second, the Heston model includes an additional Brownian motion that allows volatility to mean-revert.
• • Third, these Brownian motions are linked by a correlation.

Sample code is provided to run the Heston model. The corresponding implied volatilities are graphed and shown to replicate the volatility smile.

In this course, we'll address the basics of option pricing. We'll provide a short review of discounting and future value and also discuss the Law of No-arbitrage, along with examples that illustrate its utility in pricing.

We will also define two basic option types, call and puts, and explain their payoffs. The six key inputs that determine option prices will be examined and the relationship of each input’s effect on the call price and put price will be evaluated. The survey of the types of participants in options markets will also be discussed. The trading strategies used by these participants will be presented, both with single options, as well as with combinations of options. Next, option pricing will be analyzed in detail. First, a binomial model is used to compute the price of an option in discrete time. The underlying assumption of no-arbitrage is addressed again as the option is priced going backward in time, from option expiration to the present. The hedge ratio at each node is calculated to emphasize the notion of replication. Then the Black Scholes formula will be derived, along with explanations of the assumptions underlying the model. The mathematics are carefully interpreted at each step, resulting in an intuitive description of the partial derivatives, or Greek sensitivities, within the Black Scholes partial differential equation.

Swaps are the most prevalent derivatives used by corporations, and financial institutions to exchange a set of future cash flows with another set. The market participants carry them in balance sheet or off-balance sheet, and their gigantic volume has always been a point of concern for regulatory bodies and central banks. Considering that FRA is based on the exchange of one cash flow with another one, swap is set of FRAs.

In this course, we will discuss the basic financial theories and concepts relevant to swaps. The pricing of swaps will also be explained and demonstrated through many examples. We then look into Interest Rate including Forward and Overnight Index Swap (OIS) swaps, Equity, Cross-Currency, Quanto, Credit Default, and Asset Swaps.

The Credit Default swaps (“CDS”) are now extremely popular and trade billions of dollars every day. While they were originally developed to hedge the risk of fixed income products, they are now used to take a position without trading the underlying which can be a particular bond of a corporation or a country. Interestingly, the size of a particular CDS can many times be larger than the size of the underlying because they are cash-settled. Therefore, we will spend a good portion of our time on this subject.

Credit Default Swaps (“CDS”) allow investors to swap the credit risk of a corporation, index, or a country with other investors. CDS market started in 1990’s and drastically grew until 2007 global crisis to a $60 trillion market. For comparison, the global equity and bond markets are about $80 and $90 trillion respectively. Considering the important role that CDS played in shaping the global crisis of 2007 and also the large trading loss at JP Morgan, the governments introduced more restrictions on the CDS market. CDS which were mainly traded as OTC products between brokers and clients, were then transformed to become more standard contracts clearing via central clearing counterparties.

Ready to earn a professional certificate and stand out in your field?

If you’ve gained a clear, comprehensive understanding of the courses, your next step is to complete the Derivatives Professional Certificate Examination from the New York Institute of Finance.

The exam comprises 30 questions, timed at 60 Minutes. To qualify for the certificate, learners must receive a grade of at least 70% or better.

Prerequisite for this exam:

Earn a Verified Certificate in all parts of the Derivatives program from NYIF:

1. 1. Forwards and Futures
2. 1. Swaps Fundamentals
3. 1. FX Markets Derivatives, Cross Currency Swaps, and Credit Derivatives
4. 1. Option Contracts, Participants, Strategies, and Pricing
5. Greeks, American Options, and Volatility