### Questions

**1)** What is an Option ?

An agreement that gives the investor the right (but not the obligation) to buy (or sell) an asset at a specific price on a particular date in the future.

**2)** Why would someone buy an Option ?

If you have a commitment to buy something in the future you can buy an option contract to provide some protection against the price that you will have to pay.

When this day comes you can compare the current price with the price stated in the option contract.

If the current price is higher than the option price then you can execute the option which allows you to buy at the lower price.

**3)** What is a Call Option ?

A Call Option gives the investor the right (but not the obligation) to buy an asset at a specific price on a particular date in the future.

**4)** What is a Put Option ?

A Put Option gives the investor the right (but not the obligation) to sell an asset at a specific price on a particular date in the future.

**5)** What do the following abbreviations means:

Long Call - buying a call option

Short Call - selling a call option

Long Put - buying a put option

Short Put - selling a put option

**6)** What information do you need to price an option ?

*) Price of the Underlying Asset

*) Volatility of the Underlying Asset

*) Risk Free Interest Rate

*) Strike Price (the agreed price the asset can be bought or sold at)

*) Maturity Date

Dividend information if the asset is an Equity

Coupon rate if the asset is a Bond

**7)** What is the difference between a European Option and an American Option ?

A European option can only be exercised on the maturity date where as an American option can be exercised at any time.

**8)** Under what circumstances would you exercise an American Call Option on an Equity that pays no dividend ?

Never. American options are rarely exercised early.

All options have a positive time value and are usually worth more not exercised.

Owners who want to close out of an option position would prefer to sell it and sacrifice "some" time value rather than exercise early and sacrifice "all" the time value.

**9)** What is the Drift ?

This is a measure of the average rate of growth of the underlying asset.

**10)** What is the Option Premium ?

This is the price of the option contract.

**11)** What aspects do you have to consider when buying and selling options ?

Premium - The amount charged for the right

Strike Price - The agreed price the asset can be bought or sold at

Maturity Date - The date when the option can be exercised

Historical Volatility - derived from past data, usually the previous x number of daily closes

Implied Volatility - considers past data and also takes a view on the future

**12)** What is Historical Volatility ?

This is the annualized standard deviation of past stock price movements.

It measures the daily price changes in the stock over the past year.

**13)** What is Implied Volatility ?

This is derived from an option's price and shows what the market "implies" about the underlying asset's volatility in the future.

Implied volatility shows the market's opinion of the asset's potential movement in the future.

It does not forecast direction.

**14)** Why is the Implied Volatility so important ?

The higher the Implied Volatility, the higher the option premium.

When the price of the underlying falls, the implied volatility increases ?

When the price of the underlying increases, the implied volatility decreases ?

Knowing where implied volatility levels are and where they are likely to go, can make a substantial difference to the outcome of a strategy.

Implied volatility offers an objective way to test forecasts and identify strategy entry and exit points.

**15)** How can you calculate Implied Volatility ?

Implied Volatilty can not be observed in the market and can only be determined by knowing all the other variables and using a model.

The Black Scholes Model is modified so market price becomes an input and volatility is the output.

The most traded options are the ones that are 'at-the-money' so it is these ones that are generally used in a model.

**16)** What is a Volatility Smile ?

These are implied volatility patterns that arise in pricing options.

Graphing the implied volatility against different strike prices for a given expiry produces a skewed smile instead of the expected constant volatility.

When there are higher prices for 'out-of-money' options this implies a deficiency in the Black Scholes Model which assumes constant volatility.

**17)** What is an 'Uncovered' Option ?

This is an option that is not backed by the an offsetting position in the underlying.

Also known as a naked option.

**18)** What is a 'Barrier' Option ?

Similar to a plain vanilla option but with the presence of one or two trigger prices.

If a trigger price is touched the option is either activated or erased.

A single barrier has one trigger price.

A double barrier has two trigger prices.

**19)** Can you describe the main types of Barrier Options ?

Up and Out - barrier level is higher than spot (option is erased)

Down and Out - barrier level is lower than spot (option is erased)

Up and In - barrier level is higher than spot (option is activated)

Down and In - barrier level is lower than spot (option is activated)

**20)** Why would someone buy a Barrier option ?

These are cheaper than vanilla options.

**21)** What is a 'Lookback' option ?

The payoff is the highest or lowest price that the spot trades at over the life of the option.

Lookback Call - right to buy at a strike price equal to the lowest price the spot traded at.

Lookback Put - right to sell at a strike price equal to the highest price the spot traded at.

**22)** What is an 'Asian' option ?

This type of option has its payoff determined by the average price of the underlying over a defined period.

**23)** What is a 'Quanto' option ?

The underlying is denominated in one currency but the instrument is settled in a different currency at some fixed interest rate.

Also known as a Fixed Exchange Rate Option or a Foreign Asset Option.

**24)** What is a 'Composite' option ?

The underlying is denominated in one currency but the instrument is settled in a different currency. The interest rate is not fixed but floating

Also known as a Floating Exchange Rate Option or a Foreign Asset Option.

**25)** What is a 'Rainbow' option ?

This type of option is exposed to two or more sources of uncertainty.

A normal option is exposed to one, normally the price of the underlying.

A good example might be to value natural resources deposits. Such assets are exposed to two uncertainties - price and quantity.

**26)** Can you draw the payoff diagram for buying a European call option ?

payoff = max(Current Price - Strike Price, 0)

**27)** Can you draw the payoff diagram for selling a European call option ?

payoff = -max(Current Price - Strike Price, 0)

**28)** Can you draw the payoff diagram for buying a European put option ?

payoff = max(Strike Price - Current Price, 0)

**29)** Can you draw the payoff diagram for selling a European put option ?

payoff = -max(Strike Price - Current Price, 0)

**30)** What is the Put-Call Parity ?

This is a relationship that must exist between the price of a European Call option and the price of a European Put option that has the same exercise price and maturity date.

It says that: if I buy a call option and an amount of cash equal to the present value of the exercise price then this gives me exactly the same payoff as selling a put option and buying the actual asset.

If this relationship did not exist then there would be an opportunity for risk-less profit (or arbitrage).

**31)** Can you explain the concept of moneyness ?

This describes whether an option is 'in', 'at' or 'out' of the money.

**32)** What is an 'in-the-money' option ?

An option is described as in-the-money when there would be a positive cash flow if exercised.

A Call option is in the money when Current Price > Strike Price

A Put option is in the money when Current Price < Strike Price

**33)** What is a 'deep-in-the-money' option ?

An option is described as deep-in-the-money when there is big difference between the strike price and the current price of the underlying asset.

These options trade at (or very close) to their intrinsic values.

As an option moves deeper into the money, the delta approaches 1 which means for every point change in the price of the underlying, there is an equal and simultaneous change in the price of the option in the same direction.

**34)** What is an 'at-the-money' option ?

An option is at-the-money when the strike price is very close to the current price of the underlying asset.

An option is at-the-money when Current Price = Strike Price meaning Intrinsic Value = 0

**35)** What is an 'out-of-the-money' option ?

An option is described as out-of-the-money when there would be a negative cash flow if exercised.

Intrinsic Value = 0

**36)** What is a 'deep-out-of-the-money' option ?

An option is deep-out-of-the-money when the current price of the underlying asset is less than the strike price.

**37)** What type of options are traded the most ?

The most actively traded options are the ones that trade 'at-the-money'.

Deep in the money and deep out of the money rarely trade.

**38)** What is the Intrinsic Value ?

This is defined as the difference between the exercise price and the current price.

This is basically the amount that the option is worth.

Defined as the maximum of zero and the value the option would have if it were exercised immediately.

For example, if a call option (100 shares) has an exercise price of £30 and the share price is currently trading at £40 than the call option has an intrinsic value of (40-30) £10 (per share). If the current price is less than the exercise price the call option has no intrinsic value.

**39)** What is the Intrinsic Value of a Call Option when the Current Price > Strike Price ?

Current Price - Strike Price

This option is "in the money"

**40)** What is the Intrinsic Value of a Call Option when the Current Price < Strike Price ?

Zero

This option is "out of the money"

**41)** What is the Intrinsic Value of a Put Option when the Current Price > Strike Price ?

Zero

This option is "out of the money"

**42)** What is the Intrinsic Value of a Put Option when the Current Price < Strike Price ?

Strike Price - Current Price

This option is "in the money"

**43)** What is the Time Value ?

This is the difference between the premium (price of the option) and the intrinsic value ?

**44)** What are the risk measurements (sensitivities or greeks) ?

Delta - This is the amount an option price is expected to move for a 1 dollar change in the underlying. Calls have a positive delta. Puts have a negative delta.

Gamma - This is how fast the delta is changing

Vega - How the price of the option changes with volatility

Rho - How the price of the option changes with interest rates

Theta - How the price of the option changes with time

Quoted in terms of 1 day.

**45)** What would the delta be for the following types of options at expiry ?

Call Option - In the Money: 1

Call Option - Out of the Money: 0 (zero)

Call Option - At the Money: 0.5

Put Option - In the Money: -1

Put Option - Out of the Money: 0 (zero)

Put Option - At the Money: -0.5

**46)** Can you describe some Option Strategies ?

(Covered Call) - buy asset, sell call option (neutral position)

(Married Put) - own asset, buy put option (bullish, hope price increases)

(Bull Call Spread) - buy call option, sell call option at a higher exercide price (bullish)

(Bear Put Spread) - buy put option, sell put option at a lower exercide price (bearish)

(Protective Collar) - buy 'out of the money' put option, sell 'out of the money' call option (locks in profit after a long position has made gains)

(Long Straddle) - buy call and put simultaneously with same strike (hope price will move in either direction)

(Long Strangle) - buy call and put simultaneously with put strike below call strike (hope price moves significantly in either direction)

(Butterfly Spread) - combination of a bull spread and a bear spead using 3 different strike prices

(Iron Condor) - combination of two different strangle positions

(Iron Butterfly) - combination of a long or short straddle with a buy or a sell of a strangle

**47)** How do you price a European Option on an Equity ?

There are a number of different approaches

Black Scholes - (PDE, analytical closed form solution)

Blacks -

Binomial Tree - (Numerical Method) slow (trinomial trees)

Finite Differences - (Numerical Method)

Monte Carlo - (Numerical Method) extremely slow

Risk Neutral Valuation - (Numerical Method)

**48)** How do you price an American Option on an Equity ?

Black Scholes -

Binomial Tree (Numerical Method)

Implicit Finite Differences - (Numerical Method)

Monte Carlo - (Numerical Method) - You must obtain the optimal exercise threshold function

Least Square Method -

Whaley -

**49)** How do you price a European Option on a Bond ?

There are three different approaches which you could use:

*) Ignore the Term Structure - Black Scholes because it has an assumption that the risk free interest rate is constant

*) Model the Term Structure - continuous models

*) Match the Term Structure - discrete models

**50)** Can you use the Black Scholes model to price an Option on a Bond ?

No. There are three reasons why this is not a suitable model.

*) The model assumes that the volatility of the underlying is constant. As a bond moves closer to maturity the price volatility decreases.

*) The probability distribution assumes lognormal which means the price can take on any positive value. The price of a bond can never exceed the sum of the coupons plus the principle. The black-scholes model can produce a price that exceeds this.

*) The model assumes that the risk free interest rate is constant. A change in the short term interest rate will affect the other interest rates along the yield curve.

**51)** Can you use Binomial Trees based on Prices to price an Option on a Bond ?

No. This model suffers from the same problems as the Black Scholes model.

**52)** Can you use Binomial Trees based on Yields to price an Option on a Bond ?

No. This model does not satisfy the put-call parity relationship and therefore allows arbitrage opportunities.

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