Options

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Types of Options



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Combination of Underlying Asset and an Option:

Covered Call:      A Long Position in the stock accompanied by short sale of a call to collect the option premium.




Protective Put:   A Long Position in the stock accompanied by purchase of a put to protect the downside.


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Put - Call Parity





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Two Classes of Options - Straddle & Strangle

Combine a call and Put with the same strike price and maturities called  straddle
Long Straddle : Buying a call and a put with the same maturity and strike price.
Short Straddle : Selling a call and a put with the same maturity and strike price
Straddle will benefit from a large price move up or down.

Combine a call and Put with the different strike price and maturities called  Strangle




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One Class of Options  - Spreads

Vertical Spreads refers to different strike prices
Horizontal Spreads refers to different Maturities
Diagonal Spreads move across maturities and strike prices.

Bull spread -  is positioned to take advantage of an increase in price of the underlying asset.
Bear spread - is bet on a falling price.

Spreads involving more than 2 positions are referred to as butterfly or sandwich spreads.

Butterfly spread involves three types of options with the same maturity.
a long call at a strike price K1
two short calls at a higher strike price k2,
long call at a even higher strike price k3.

Sandwich spread is a opposite of butterfly spread.

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The Basel II Capital Accord [63] identifies
three main sources of risk: credit risk, market risk and operational risk.


Credit risk is typically represented by means of three factors:
default risk,loss risk and exposure risk.



Risk management is primarily concerned with reducing earnings volatility
and avoiding large losses.

In a proper risk management process, one needs
to identify the risk, measure and quantify the risk and develop strategies to
manage the risk.


Risk management is primarily concerned with reducing earnings volatility
and avoiding large losses. In a proper risk management process, one needs
to identify the risk, measure and quantify the risk and develop strategies to
manage the risk.

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Bank Stress Testing

VAR does not purport to account for extreme losses.This is why VAR should be complemented by stress testing which aims at identifying situations that could create extraordinary losses for the institution.

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Stress testing is a key risk management process which includes

1. scenario analysis : it consists of evaluating the portfolio under various states of the world.

2. stressing models :  it involves evaluating the effect of changes in valuation models, as well as in inputs such as volatilities and correlations.

3. developing policy responses consists of identifying steps the bank can take to reduce its risk and converse capital.

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Stress tests fall into three categories:

These scenarios can be created using a variety of methods.

a.  Scenarios requiring no simulation : 

     This approach is backward looking and does not account for changes in portfolio composition.

b.   Scenarios requiring a  simulation: 

These consist of running simulations of the current portfolio subject to large hsitorical shocks - for example stock market crash of 1987 , the ERM criseis of September 1992, the bond market rout of 1994 and so on.

c.   Bank-specific scenarios : 

Creating prospective scenarios should be tailored to the portfolio at hand.

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Stress-testing is useful to guard against event risk.

Goal of Stress-testing is to identify areas of potential vulnerability.

The objective of stress-testing and management response should be to ensure that the institution can withstand likely scenarios without going brankrupt.

Institutions should stress-test their market and credit exposure, taking into account the concentration risk to groups of counter parties and the risk that liquidating positions could move the markets.

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Normal Distribution & Non Normal Distribution - (Skewness & Kurtosis)

The skewness measures the asymmetry of a probability distribution around its mean. 
Decline in the asset prices is more severe than increases.

Kurtosis measures the distribution around the mean; a high kurtosis has fatter tail ends of the distribution, and a low kurtosis has skinny tail ends of the distribution. 
Having more probability weights (observations) in its tails in relative to the normal distributions.

Expected Loss - Credit Risk

1. PD The probability of default of a borrower over a one-year horizon.

2. LGD The loss given default (or 1 minus recovery) as a percentage of exposure at default

3. EAD Exposure at default (an amount, not a percentage)

4. Maturity



For a given maturity, these parameters are used to estimate two types of expected loss (EL).



Expected loss as an amount: EL =  PD x LGD x EAD  


expected loss as a percentage of exposure at default: EL% = PD x LGD .


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 Measurement and Estimation of LGD.

 Loss given default includes three types of losses:

• The loss of principal
• The carrying costs of non-performing loans, e.g. interest income foregone
• Workout expenses (collections, legal, etc.)


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Source -

http://fic.wharton.upenn.edu/fic/papers/04/0401.pdf
http://riskarticles.com/credit-risk-how-to-calculate-expected-loss-unexpected-loss/
https://www.riskprep.com/all-tutorials/37-exam-31/114-default-correlations
http://www.quantatrisk.com/python-for-computational-finance/


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Forwards vs Futures ; Types of Derivatives

There are two types of derivatives – linear and non-linear. Linear derivatives involve futures, forwards and swaps while non-linear covers most other derivatives.