By Kerry Back
"Deals with pricing and hedging monetary derivatives.… Computational tools are brought and the textual content includes the Excel VBA exercises equivalent to the formulation and systems defined within the e-book. this can be worthy on the grounds that machine simulation can assist readers comprehend the theory….The book…succeeds in providing intuitively complicated spinoff modelling… it presents an invaluable bridge among introductory books and the extra complex literature." --MATHEMATICAL REVIEWS
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Extra info for A course in derivative securities : introduction to theory and computation
The value of the option at maturity is max(0, S(T ) − K). Consider a contract that pays S(T ) at date T when S(T ) ≥ K and that pays zero when S(T ) < K, and consider another contract that pays K at date T when S(T ) ≥ K and zero when S(T ) < K. In Chap. ” The call option is equivalent to a portfolio that is long the ﬁrst contract and short the second, because the value of the call at maturity is S(T ) − K when S(T ) ≥ K and it is zero otherwise. So, we can value the call if we can value the share digital and the digital.
5) A European put option pays K − S(T ) at date T if S(T ) < K and 0 otherwise. As before, let y= 1 if S(T ) < K , 0 otherwise . The payoﬀ of the put option is yK − yS(T ). This is equivalent to K digitals minus one share digital, all of the digitals paying when S(T ) < K. 4) and d2 = d1 − σ T . 6) Again, this is the Black-Scholes formula. The values of the European put and call satisfy put-call parity, and we can also ﬁnd one from the other by2 e−rT K + Call Price = e−qT S(0) + Put Price . ” This measures the sensitivity of the option value to changes in the value of the underlying asset.
2. Repeat the previous problem for the function X(t) = t3 . In both this N and the previous problem, what happens to i=1 [∆X(ti )]2 as N → ∞? 3. Repeat the previous problem to compute i=1 [∆B(ti )] , where B is a simulated Brownian motion. For a given T , what happens to the sum as N → ∞? 4. Repeat the previous problem, computing instead i=1 |∆B(ti )| where | · | denotes the absolute value. What happens to this sum as N → ∞? 5. Consider a discrete partition 0 = t0 < t1 < · · · tN = T of the time interval [0, T ] with ti − ti−1 = ∆t = T /N for each i.