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QFD Formulas

Manuel Gulino Mathematics Englisch 53 Karten

QFD Formulas

Karten in diesem Stapel (53)

  1. 1VAR[dWt]T-t
  2. 2E[dWt]0
  3. 3dSt Bachelier E[ST] = ?dSt Bachelier E[ST] = ?
  4. 4dSt Bachelier VAR [ST] = ?dSt Bachelier VAR [ST] = ?
  5. 5dSt Bachelier ST = ?dSt Bachelier ST = ?
  6. 6How is dSt distributed under Bachelier?How is dSt distributed under Bachelier?
  7. 7How is ST distributed under Bachelier? (suppose t = 0)How is ST distributed under Bachelier? (suppose t = 0)
  8. 8Ito Formula under BachelierIto Formula under Bachelier
  9. 9Define d ln(St) under Black and Scholes. What is its expected value and variance?Define d ln(St) under Black and Scholes. What is its expected value and variance?
  10. 10How is ST defined in Black and Scholes?How is ST defined in Black and Scholes?
  11. 11dSt Black and Scholes E [ST] = ? VAR [ST] = ?dSt Black and Scholes E [ST] = ? VAR [ST] = ?
  12. 12dSt Black and Scholes Discounted stock pricedSt Black and Scholes Discounted stock price
  13. 13Black and Scholes: Ito FormulaBlack and Scholes: Ito Formula
  14. 14Ito Formula Option with multiple assetsIto Formula Option with multiple assets
  15. 15Black and Scholes PDEBlack and Scholes PDE
  16. 16How do you obtain the BS PDE?How do you obtain the BS PDE?
  17. 17EU CallEU Call
  18. 18EU PutEU Put
  19. 19Define d1 and d2 in the risk neutral valuation of european optionsDefine d1 and d2 in the risk neutral valuation of european options
  20. 20Asset or Nothing CallSo * N(d1)
  21. 21Cash or Nothing CallK*e^(-rT) * N(d2)
  22. 22Cash or Nothing PutK*e^(-rT) * N(-d2)
  23. 23Asset or Nothing PutSo * N(-d1)
  24. 24Risk Neutral Probability in Cox Ross Rubinstein (q)Risk Neutral Probability in Cox Ross Rubinstein (q)
  25. 25EU Option under CRREU Option under CRR
  26. 26US Option under CRRAt each node you take the highest between the EU price and the Intrinsic Value of the option (S-K for Calls, K-S for Puts)US Option under CRR
  27. 27Lookback Options under CRRConsider all possible paths to each final payoff. For each path, take the lowest St for a Call and the highest St for a Put.
    Then discount the product of the probabilities multiplied by the sum of the intrinsic values for each possible path.
  28. 28Replicating strategy of an option in CRRReplicating strategy of an option in CRR
  29. 29Replicating strategy of a portfolio in CRRReplicating strategy of a portfolio in CRR
  30. 30Describe the different GreeksDelta: sens of option to underlying
    Theta: sens of option to time.
    Gamma: sens of delta to underlying (convexity)
    Vega: sens of option to volatility.
    Rho: sens of option to interest rate.
  31. 31Delta Neutrality with Gamma in a rangeDelta Neutrality with Gamma in a range
  32. 32Delta Gamma Vega NeutralityDelta Gamma Vega Neutrality
  33. 33Term Structure of Interest RatesBasically BS PD but with drift = u - lambda*sigma
    i.e. the market price of risk
    rt not multiplied    Term Structure of Interest Rates
  34. 34When does rt admit an Affine Term Structure?When does rt admit an Affine Term Structure?
  35. 35Vasicek ATSVasicek ATS
  36. 36Vasicek CALL Hull White Vasicek CALLVasicek CALL Hull White Vasicek CALL
  37. 37Ho Lee ATSHo Lee ATS
  38. 38Ho Lee CALLHo Lee CALL
  39. 39CIR ATSCIR ATS
  40. 40Greeks of Cash or Nothing PutGreeks of Cash or Nothing Put
  41. 41Hull White ATSHull White ATS
  42. 42MartingaleMartingale
  43. 43Supposed you have a Bachelier model. How do you compute the probability of an event?Compute the probability, e.g Xt < 5, then
    Isolate dWt and standardize.
  44. 44Greeks of Cash or Nothing CallGreeks of Cash or Nothing Call
  45. 45what happens to the delta of a cash or nothing Call Option in the limit t-> oo : 1 - When St is close to K 2 - When St is far from K1 - Delta Very Large (Pin Risk)
    2 - Delta Close to 0
  46. 46What is the interval of St for which the vega of a cash or nothing call option is negative?vega is positive when S < K (out the money)
    Negative for S > K (in the money)
    Study the sign of d2
    denumerator always positive, so to be negative the numerator must be negative
  47. 47Greeks of Asset or Nothing CallGreeks of Asset or Nothing Call
  48. 48Greeks of Asset or Nothing PutGreeks of Asset or Nothing Put
  49. 49Vasicek a(b-rt)dt + ... rt = ? E[rt] = ? VAR [rt] = ?Vasicek a(b-rt)dt + ... rt = ? E[rt] = ? VAR [rt] = ?
  50. 50delta gamma vega of eu optionsdelta gamma vega of eu options
  51. 51Log propertiesLog properties
  52. 52Derivate: -esponenziale composta - prodotto - quozienteDerivate: -esponenziale composta - prodotto - quoziente
  53. 53Trasformare tasso di interesse annuale in quello di un altro periodoTrasformare tasso di interesse annuale in quello di un altro periodo

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Beschreibung
Mathematics Karteikarten am QFD Formulas, erstellt von Manuel Gulino am 15/12/2022.
Erstellt von
Manuel Gulino
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