LIBOR market model

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The LIBOR market model, also known as the BGM Model ( Brace Gatarek Musiela Model , referring to the names of some inventors) is a financial model of interest rates. It is used for price interest derivatives, especially exotic derivatives such as swivel swaps, ratchet and floor caps, target redemption records, autocaps, zero coupon swaps, constant maturity swaps and deployment options, among many others. The number modeled, rather than the short-level or the instant forward level (as in the Heath-Jarrow-Morton framework) is a set of advanced levels (also called forward LIBORs), which have the advantage of being directly observable in the market. , and its volatility is naturally associated with contracts traded. Each forward rate is modeled by a lognormal process below the front, ie the Black model leading to the Black formula for the interest rate limit. This formula is the market standard for quoting hat prices in terms of implied volatility, hence the term "market model". The LIBOR market model can be interpreted as a collection of forward LIBOR dynamics for various forward rates with tenor and maturity ranges, each forward rate consistent with the Black-based caplet formula for canonical maturity. One can write different tariff dynamics below the general pricing measure, such as the front size for the preferred single maturity, and in this case the forward rates will not be lognormally below the unique size in general, leading to the need for numerical methods such as monte carlo simulation or estimates such as frozen drift assumptions.

Video LIBOR market model

Model dinamis

Model pasar LIBOR memodelkan satu set ${\ displaystyle n}  ÂÂ$ forward rates ${\ displaystyle L_ {j}}  ÂÂ$ , ${\ displaystyle j = 1, \ ldots, n}  ÂÂ$ sebagai proses lognormal. Di bawah masing-masing ${\ displaystyle T_ {j}}  ÂÂ$ -Untuk ukuran ${\ displaystyle Q_ {T_ {j 1}}}  ÂÂ$

${\ displaystyle dL_ {j} (t) = \ sigma _ {j} (t) L_ {j} (t) dW ^ {Q_ {T_ {j 1} }} (t) {\ text {.}}}  ÂÂ$

Source of the article : Wikipedia