Options, Volatility 1

8/8/2019 Options, Volatility 1

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Currency OptionsCurrency Optionsy Currency options trade on the

Philadelphia Exchange (PHLX)y

There also exists a very active over-the-counter (OTC) markety Currency options are used by

corporations to buy insurance when they

have an FX exposure


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Currency optionCurrency option- - Exporter Exporter

perspcetiveperspcetivey A US exporter, exporting to Australia,expects to receive 10 Mn AUD in 3 monthstime.

y The 3m Forward rate is 0.700 USD/AUD.y The exporter buys a 3 month put option on

AUD, with K =0.7000.y After 3 months, if exchange rate isy A) 0.67000 USD/AUD.y B) 0.73000 USD/AUD.y Gain/Loss to exporter on option contracty


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Currency optionCurrency option- - Importer Importer

perspectiveperspectivey A US importer, importing from Europeanmanufacturer and is expected to pay 1MnEuro for imported cargo, arriving in 3

months time.y The 3m Forward rate is 1.200 USD/Euro.y The exporter buys a 3 month call option on

Euro, with K =1.200y After 3 months, if exchange rate isy A) 1.2500 USD/EURy B) 1.1500 USD/EURy Gain/Loss to importer on option contract


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Range Forward ContractsRange Forward Contractsy Here on option is bought and another option

sold, such that the price of the bought optionequals the price of the sold option. (Buying acall option with strike price K1 and selling a putoption with strike price K2).

y A US Exporter buying a put option on Euro withstrike price K1 = 1.8500USD/EUR and selling acall option with strike price K2= 1.9500USD/EUR.

y The current 3 month forward rate is1.9200USD/EUR.

y


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y Have the effect of creating a costlesshedging structure.

y Ensures that the exchange rate paid or

received will lie within a certain range.y When currency is to be received it involves

buying a put with strike K 1 and selling a callwith strike K 2

y When currency is to be paid it involvesselling a put with strike K 1 and buying a callwith strike K 2 (with K 2 > K 1 )


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Range Forward ContractRange Forward Contract

Payoff

AssetPrice

K 1 K 2

Payoff

AssetPrice

K 1 K 2

ShortPosition

LongPosition


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Exotic optionsExotic optionsy These are basically structured options,

used for specific purpose.y 1)Asian optionsy 2) Barrier optionsy 3) Basket optionsy 4) Swing Options


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VolatilityVolatilityy Volatility is the uncertainity about the returns

provided by underlying asset.y The volatility is the standard deviation of the

continuously compounded rate of return in 1year.

y The standard deviation of the return in time ( t is t (W

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Estimating Volatility from HistoricalEstimating Volatility from Historical

DataData1. Take observations S 1 , . . . , S n on the

variable at end of each trading day2. Define daily return as:

Calculate the standard deviation, s , of

the u i sThe historical volatility per year estimateis:

uS

S ii

i

!

l n

1

252v s

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Market Implied volatilityMarket Implied volatilityy The volatility implied from market prices of

options are called implied volatility.y The implied volatility of an option is the volatility

for which the Black-Scholes price equals themarket pricey It measures, the market expectation of the future

volatility of the underlying.y Implied price distribution are different than Log

normal distribution.

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The Volatility SmileThe Volatility Smile

Implied

Volatility

StrikePrice

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Volatility Term StructureVolatility Term StructureThe volatility term structure tend to bedownward sloping when volatility is highand upward sloping when it is low

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Volatility SurfaceVolatility Surfacey It combines volatility term structure and volatilitysmile in a matrix form.

y The columns reflect volatility term structure &

rows reflect volatility smile, across differentstrike rates.

y This volatility matrix is used by traders for

valuing options with different strike prices andmaturity.

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Example of a Volatility SurfaceExample of a Volatility Surface

S t r ik e P r ic e

. . . . .

m t . . . . .

m t . . . . .

m t . . . . .

ye a r . . . . .

ye a r . . . . .

ye a r . . . . .

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Options, Volatility 1