# Best way To Learn Finance? Understand Market Data

Financial institutions consume market data on continuous basis to value their portfolios. As human body cannot function without blood, financial institutions cannot value their portfolios without market data. Therefore, understanding market data is the key to calculate risk and return of financial transactions and it can also help us understand finance in general.

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I encourage everyone to understand market data.

A large number of models and mathematical formulae are implemented to price a transaction in a portfolio. These models rely on market data.

### Importance of Market Data

In my previous articles “What is an Interest Rate Swap?”, “Options & Trading Strategies” and“Bond Price And Risk”, I explained how to price and calculate risk of a number of financial transactions. Market data is used as an input to value a transaction. Subsequently, it can help financial institutions take calculated decisions to increase return and hedge risk.

### Market Data Types

Market data is composed of a large family of components. In this article, I will explain foreign exchange rates, yield curves and volatility surfaces. Additionally I will briefly outline purpose of spreads.

Let’s Start With Foreign Exchange Rates

### Foreign Exchange Rates

Foreign exchange (FX) rate is a numerical value that is used to convert an amount in one currency (domestic currency) into an equivalent amount in another currency (foreign currency). Exchange rates change on timely basis.

Exchange rates are crucial in pricing trades where multiple currencies are involved. For instance to price a FX Forward or Cross Currency Swap, spot exchange rates of the currencies are used to convert an amount in one currency to another currency. Exchange rates reflect trading activity. They are based on a number of factors including supply-demand and current investments. Unlike stocks, exchange rates are not traded in exchanges. Exchange rates are volatile and frequently move from one level to another.

Exchange rates are usually quoted as bid-offer rates per currency. The distance between bid and offer rates can help us understand volatility of a currency and how stable a currency is. Spot exchange rate is one-dimensional in nature. To elaborate, exchange rate is represented as one value per currency. As an instance, for domestic currency GBP, we can represent foreign exchange rates as

EUR = 2, USD = 3, AUD = 1.5, INR = 100 and so on.

These hypothetical rates represent value of 1 GBP in the respective foreign currencies.

### Example 1 — Basic Calculation

Let’s assume we go to a high street exchange broker to convert £100 to Euros. For the sake of simplicity, let’s also assume that the exchange rate is the average of bid and offer rates. The current exchange rate from GBP to EUR is 2 GBP/EUR. This means, for every 1 pound that we pay, we will receive 2 Euros in return. *In the example above, GBP is the domestic currency and EUR is the foreign currency.*

Therefore for the £100, we will receive 200 Euros.

### Example 2 — Exchange Rate Triangulation

We can use a combination of exchange rates to compute exchange rates for other currencies. Based on the exchange rates information above, how many Indian Rupees (INR) should we get for 150 Australian Dollars (AUD)?

According to the information above:

- 1 GBP = 100 INR
- 1 GBP = 1.5 AUD

Therefore 1 AUD = (100/1.5) = 66.7 INR.

As a result, 150 AUD = 66.7 x 150 = 10005 INR (approx).

We can also gather exchange rates over a period of time and calculate valuable statistical measures such as mean, max/min, volatility etc. on the data. These measures then help analysts forecast exchange rates.

Furthermore, interest rate parity, volatility and correlation between exchange rates also exist which are used to simulate exchange rates for future time points. Forecasting and stimulating exchange rates is beyond the scope of this article.

To summarise, we learnt what exchange rates are and how amounts in one currency can be converted to another currency.

The next part will concentrate on interest rate curves which are also known as yield curves.

### Yield Curves

Yield curve is an important market data component. Yield curve tells us the relationship between interest rate and the time to maturity of debt contracts. They are used in pricing bonds, swaps, options and a range of important transactions.

Interest rates help us understand price and value of money. Subsequently, interest rate is the cost of borrowing money.

For example, yield curve is used to determine the amount a bank will charge a borrower to borrow money for contracts of different maturities. Yield curves are two dimensional, they plot interest rates for a range of contract maturities.

As an instance, the chart above shows an hypothetical yield curve. X axis shows the length of the borrowing contract. It indicates that a bank will charge roughly 2.7% interest for borrowing money for 1 year.

Yield curves help investors understand economical situation of a country as interest rate curves are influenced by a number of factors including supply and demand, credit worthiness, whether country wants to raise its reserves, price of Government bonds etc. Higher government rates are usually better for investors who wish to invest their money in banks and earn profit from the interest rates whereas lower interest rates imply that the cost of borrowing money is cheap. As a consequence, lower interest rates help borrowers to borrow money. It increases outflow of money in a bank.

### Yield Curve Attributes

Interest rate curve has a number of attributes for example curve name, currency, maturity etc. Maturity of the curve is also known as term e.g. 6M which indicates length of the contract. Usually, loan borrowed for longer period requires higher interest than loan required for shorter term due to greater risk and uncertainty in lending money for longer term.

Interest rate curve has a number of interest rate points where each point is two dimensional and contains Year Fraction and Interest Rate Value properties.

Year Fraction is the fraction in years for borrowing money from today to some date in the future e.g. Year Fraction to borrow money for 6 months will be 0.5 years.

Spot yield curve for a currency can be shown in a table:

### Spot Vs Forward Yield Curves

Yield curves can be spot or forward curves. This section explains the difference between spot and forward curves.

### Spot Rates

Current interest rates for borrowing money are spot interest rates. Spot interest rates are observed in market and are available via a number of interest rates providers. Spot rates are also known as zero rates and are computed from zero coupon bond returns.

Spot rate is the rate lenders charge on loan to be taken immediately.

For example, imagine you want to borrow £1000 from a bank for 1 year. Also assume bank offers interest rate of 8% for 6 months and 10% for 1 year. This means that if you borrow money for 1 year then you will pay the bank 10% of interest. Therefore, the bank expects you to pay £1000 + 10% interest in a year’s time. As a result, you will pay the bank back

£1000 x (100%+10%) = £1100

£100 is the cost of borrowing £1000 for a year.

If you borrow the same amount for 6 months then you will pay £1000 x 8% x 0.5 because 8% is the interest rate for borrowing money for 6 months.

This calculation assumes discrete compounding. To see it another way, £1100 in a year’s time is worth £1000 today. We get that figure by discounting (dividing) the amount by the interest rate for the year, for example £1100/(1.1) = £1000

Larger the interest rate, smaller the future value of money

### Yield Curve Example — Spot Rate

Imagine you invest £1000 in a bank today that offers 10% interest rate for a year. After a year, you will receive £1000*(10%+100%) = £1100 from the bank.

### Forward Rates

Forward rates are calculated by extrapolating current spot rates. They are computed such that the future interest rates do not introduce arbitrage opportunities. Forward rates are the **agreed** interest rates. If someone wants to borrow money in future for a specified amount of time then forward rate is used. Forward rates are also known as future implied spot rates. Price of transactions that require delivering currency or commodity in near future is based on forward rates.

### Yield Curve Example — Forward Rates

In the spot rate example above, we invested £1000 for a year and received £1100 after a year due to 10% interest rate. Assume instead of investing £1000 for a year, you decide to invest the money in a bank for 6 months at 8% interest and then reinvest again for 6 months. 8% is the 6 month spot interest that the bank offers.

The bank should offer a 6M forward rate such that the amount of money for two six month periods after a year should be equivalent as you investing your money straight for 1 year at 10%. If both of the amounts are not equal then the investor can benefit and start earning profit without taking any risk.

Forward rate formula at period n = [(1+Spot Rate (n)) ^ n /(1+ SpotRate (n-1)) ^(n-1)] — 1

To calculate 6M forward rate for 1 year, formula is

Forward Rate 1Y = ((1+Spot Rate 1Y/2)²/(1+Spot Rate 6M/2)) — 1

*= ((1+10%/2)²)/((1+8%/2))-1=6%*

*We are dividing the rate by 2 because each period is 6 months long (semi-annual).*

This means, we can invest £1000 in a bank for 6 months for 8% interest and then reinvest again after 6 months for 6%. We should receive £1100 after a year. This is equivalent to us investing £1000 for 1 year for 10%.

To elaborate, we can invest £1000 in a bank for 6 months and get 8%/2 *£1000 = £40 back. Then we can reinvest for 6 months in 6 months time for 6% rate and get £1000*(1+(6%/2)²)=£1060. Total received money will still be £1100. This is the same amount which we would have received if we invested £1000 for 1 year.

### OIS And LIBOR Curve

OIS and Libor curves are the two common yield curves used in banks to price interest rate swaps. This section briefly outlines the curves.

**LIBOR curve**

LIBOR is the average interbank interest rate and comes in 7 maturities (from overnight to 12 months). LIBOR rates are registered in a number of different currencies including EUR, USD, GBP, CHF, JPY, CAD, DKK, AUD, NZD and SEK. LIBOR interest rates are essentially the rates at which selective high credit rated banks are prepared to lend money to one another. Therefore LIBOR is the rate of interest at which a bank is prepared to deposit money with other banks in Europe. It is usually higher than government yield curve because of inherited credit risk.

**OIS curve**

OIS curve is an overnight interest rate curve. OIS reflects daily change in curves. OIS curves are usually used for discounting because they are the average of daily movements in the interest rate curves and are better suited to discount collateralised trades as they are marked-to-market daily.

### Yield Curve Summary

We outlined and explained what yield curves are, their structure along with difference between spot and forward rates. Interest rates can be evolved by using a number of short term interest rate models such as Ho Lee, Hull and White, Vasicek, CIR etc. The concept of these models is beyond the scope of this article.

### Bootstrapping

Bootstrapping is a process of constructing yield curves from eligible set of financial trades that pay coupons periodically. The set of trades can include interest rate swaps, government bonds etc. with different maturities. Bootstrapping method is recursive in nature.

At a high level, the set of steps to construct a yield curve via bootstrapping methodology is:

- Select trades that pay coupons periodically. Ensure that the trades have differing maturity and their price at par is known.
- Recursively compute interest rate for periods; starting from the first period and then use the computed interest rate for the next period. Interest rate is computed by estimating the rate that gives known price of the trade.

For example, if a semi annual coupon bond maturing in six months is chosen that is priced at £100 then compute the 6M rate that will give the required price for the bond. This rate will then become the 6M spot interest rate. Now take a bond that matures in 1 year and pays semi annual coupons.

Use the rate which was computed for 6M and price of the 1 year bond to calculate the spot interest rate for second period (6M to 1Y).

These steps are applied recursively to construct a spot yield curve.

Bootstrapping technique is simple to implement and does not require optimisation techniques.

Lastly, let’s understand a third type of market data; volatility surface

### Volatility Surface

Volatility surface contains volatilities that are used to price a number of financial trades e.g. options, swaptions etc. Volatility surface can be of many types, for example FX Volatility Surface or Swaption Volatility Surface. A volatility surface has usually three dimensions: Expiry, Tenor, and Volatility Value. These volatility values are implied volatilities which are produced from market prices of options.

Before we explain the concept of volatility surface, it is important to understand the basics of Swaption and Black Scholes.

#### Swaptions:

In my article “ Options & Trading Strategies”, I explained how options work. Option is a derivative contract that gives the buyer right, but not the obligation, to buy the underlying security. At a high level, swaption is a type of option where the buyer has the right to enter into buying an underlying swap such as interest rate swap or CDS. Price of a swaption is based on many factors including properties of the underlying swap such as term of the swap contract and maturity of the option which is also known as option expiry.

An option can be priced using Black Scholes formula.

#### Black Scholes

Black scholes is a mathematical model that can give us theoretical price of options including swaptions. Volatility of an option measures how stock will move in the future. It is expressed as an annual basis in percentage. Higher the volatility, more the stock price moves.

Black scholes model assumes that the volatility is constant whereas in practice, volatility is constantly changing. As a consequence, the market price of options with the same expiry and strike price tend to diverge from their theoretic price calculated by Black Scholes formula.

There are several models implemented to estimate volatilities. One common and simple methodology is to feed the actual option’s price along with all other inputs into Black Scholes model to compute theoretical volatility that resulted in the option’s price. This volatility is known as **implied volatility.**

It is important for an investor to ensure that their portfolio’s theoretical value is as close as possible to the market value.

#### What is a volatility smile?

If we plot implied volatility for options with different strike prices, we will notice a line graph that resembles shape of a smile.

This chart is known as **Volatility Smile**. Volatility smile shows that compared to at-the-money options, volatilities are higher for deep out-of-money and deep in-the-money options.

An at-the-money option is when the strike price equals the price of the underlying asset.

#### Constructing Volatility Surface From Volatility Smile

We can start calculating volatilities for options with different strike price and expiries. Once we compute volatilities for at the money options with different expiries, we can start creating a volatility surface out of the group of volatility smiles.

- To elaborate, at the money swaption trades are selected with a range of option expiries and/or strike prices that are based on swaps over a range of tenors (or maturities). These options are used to compute implied volatility smiles.
- We then extend volatility smiles by interpolating the points using smile interpolation. Piece-wise linear interpolation is usually used due to its simplicity.
- Once a range of volatility smiles are produced for different tenors and expiry terms, we join all of the smiles on terms and tenors and plot the smiles together into a surface.

As a result, a three dimensional surface can then be created. This surface can then be used to price options. With interpolation, we can establish volatilities for a larger range of expiries and tenors.

If we plot volatility surface, where y axis is volatility point, x axis is term and z axis is tenor then we can see a volatility surface:

Volatility surfaces can also be created on different combinations such as from options with different strikes and maturities.

The table below illustrates three dimensional swaption volatility points:

### Example:

If we have been given FX volatility for two currencies and we are required to calculate volatility for the third currency then we can use volatility formula along with exchange rates triangulation to compute the required volatility.

**For example, if we have:**

- Currency 1 per Base Currency e.g. GBP per USD where USD is the base currency
- Currency 2 per Base Currency e.g. EUR per USD

Furthermore, we are required to calculate FX volatility for EUR per GBP then we can use the volatility formula with exchange rate triangulation:

*Volatility Currency 2 per Currency 1 Squared = (Volatility Currency 2 per Base Currency Squared) + (Volatility Currency 1 per Base Currency Squared )— (2 x Volatility Currency 2 per Base Currency x Volatility Currency 2 per Base Currency) x Correlation of (Currency 1, Currency 2)*

Correlation can be derived by calculating mean and standard deviation of the volatilities of each currency, potentially by using Person correlation formula.

### Spreads:

Finally, I wanted to outline role of spreads as they help us in valuing credit risk. Spread is the difference between two data points.

As an instance, government offered interest rates are considered risk-free. Financial institutions also offer interest rates to investors.

These interest rates are usually higher than the rates that government offers because of the inherit credit risk present.

Lower the credit rating, higher the rates

Financial institutions attract investors by offering higher interest rates. The difference between government rates and rates offered by financial institutions is known as “spread”. Differences of rates between two currencies is the basis spread. Difference between exchange rates bid/offer rates is bid/offer spread.

Spreads such as CDS spreads play a vital role in credit risk. Credit default Swap (CDS) is an increasingly popular structured product. It transfers credit risk from the buyer to a counterparty such as an insurance company.

For example, assume an investor buys UK bonds and he is worried that UK government might default. He can then transfer the default risk by buying a CDS from a US bank. The investor will receive coupon payments from UK bonds, he will need to pay premium payments or CDS spread to the US bank and in return US bank will guarantee payments in case UK defaults. UK government is the reference entity, UK bond is the reference asset and US bank is the insurance company.

The value of CDS spread is based on the default probability of UK Bond and the joint default correlation of US Bank and UK. Therefore, higher the probability of UK default, higher the CDS spread.

### Summary

This article highlighted importance of understanding market data components. There are number of market data providers such as Bloomberg, Markit, Timescape etc. who provide market data on timely basis. Market data plays a vital role in pricing portfolios and calculating risk.

This article outlined concepts of exchange rates, yield curves, volatility surfaces and briefly explained role of spreads.

Hope it helps. Please let me know if you have any feedback.