By Jawwad Ahmed Farid
This ebook presents a hands-on, useful consultant to figuring out derivatives pricing. aimed toward the fewer quantitative practitioner, it offers a balanced account of concepts, Greeks and hedging innovations keeping off the advanced arithmetic inherent to many texts, and with a spotlight on modelling, marketplace perform and intuition.
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Additional info for An Option Greeks Primer — Building Intuition with Delta Hedging and Monte Carlo Simulation Using Excel
Put: Put options for buyers: the right to sell an underlying security on a future date at a price agreed upon today. It gives the buyer the right to walk away if the market price is greater than the strike price. Replication: Creating a hedge for short option position that follows changes in option values. Rho: Measures the change in the value of the option due to a change in interest rates. Shadow Gamma: A calculation that takes into account changes in volatility in addition to changes in the price of the underlying.
We may understand this concept through the following simple probability example. A six-sided fair die is rolled. The probability of rolling 4 is 1/6. Now suppose we have additional information telling us that the number rolled is greater than 3. In this case, what is the probability of a 4 having being rolled? The conditional probability works out to 1/3 > 1/6. The conditional probability is higher, because we are only considering those outcomes that exceed the number 3 in our calculation. In a similar fashion, E(ST|ST > X) > E(ST) because the expected value will only consider those stock prices which exceeds the exercise price in the calculation of the expectation.
18 An Option Greeks Primer UNDERSTANDING RISK ADJUSTED PROBABILITIES THROUGH THE VALUE OF A CALL OPTION PAYMENT OF EXERCISE PRICE RECEIPT OF STOCK Payment /Receipt amount: Exercise Not exercise Payment /Receipt type on exercise Expectation of amount on exercise –X S1 0 0 Deterministic – can only take one value Probabilistic – Must therefore consider expecteed value of ST. Values of ST must be >X S1 S2 S3 –X X . ST = E[S1lST>X] Sn–4 Sn–3 Sn–2 Sn–1 > S1 S2 S3 . . ST =E[ST] . Sn–4 Sn–3 Sn–2 Sn–1 Probability: Of exercise P(ST>X) P(ST>X) Of not being exercised P(ST<=X) P(ST<=X) Discount factor e–rt e–rt Present Value=Expection* Discount Factor* Probability Comparison with Black – Scholes call option calue formula components RESULTS Figure 12 –xe–rtP(ST>X) E[S1lST>X]e–rte–rtP(ST>X) > E[ST]P(ST>X) = SP (ST>X) –xe–rtN(d2) P(ST>x)=N(d2) SN(d1) N(d1) > N(d2) N(d1) and N(d2) risk-adjusted probabilities explained Source: The Greeks against Spot.