Bank A ssetgl iab ility Sheet w ith Em bedded Op tion s

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1 : (00) , (, ) :,, ;, ; : ; ; ; ; ; : F830 : A α Con tro l O ver In terest R ate R isk of Bank A ssetgl iab ility Sheet w ith Em bedded Op tion s LU O D aw ei, W AN D ifang (Schoo l of M anagem ent, X i an J iao tong U niversity, , Ch ina) Abstract: T he bank s m ust set up the contro l system s of interest rate risk fo r that they should accep t international regulato ry standard of risk after entering W TO, and interest rate is being m arketo riented gradually, but the em bedded op tions in bank s assetgliability sheet enhance the comp lexity of interest rate risk m anagem en ṫ W e m ake researches of con tro l over in terest rate risk of bank assetgliab ility sheet w ith em bedded op tions, and select duration gap and convexity gap as the indicato rs of contro l over interest rate risk; and advance the strategies of contro l over interest rate risk under em bedded op tions, w h ich em phasize m atch ing op tion - adju sted du ration and con structing the po sitive convex ity gap to hedge the negative one; and analysis the valuation techno logy of the security w ith em bedded op tions on the basis of scene generation of interest rate, w h ich is essential to imp lem enting the strategies of con tro l over interest rate risk under em bedded op tionṡ Keywords: em bedded op tions; assetgliability; interest rate risk; duration gap; convexity gap; scene generation of in terest rate 1,,,,,, α : : ( ) ; (A. 9GL )

2 ,,,,,,,,, :, 3, 4, 5 di dv V i, V, dv D C : dv = - V D (di) V C (di) (1) dv D = - di 1 V, C = d V 1 di V. A, L E,, D A, D L de = da - dl () D E, CA, CL C E, () de = - A D A - L A D L d i A CA - L A CL (di) (3), (3), (3), D A = L D D L, CA = L A CL (4) V 0, V + V - i0, i+ i-, D = - C = V + - V - i+ - i- V + - V 0 - i+ - i0 g 1 V 0 V 0 - V - i0 - i- i+ - i0= i0- i- V 0, V + V i ig 1 V 0 5 ( ) (5) (6) 3 (3), (L ga )D L, [D A - (L ga )D L ], [CA - (L ga )CL ] (5) (6), D A

3 8 57,,, (3),,,,,,,,,,,, : 1), ; ) ; 3) 4,,,,,,,,, ,

4 H u ll W h ite : dr = [Η(t) - a r ]dt + Ρdz (7) Α Ρ Ρ, dz W iner, Η(t) t Α Η(t) gα ( ) t t,, 1 g,, , r 3, r 3 r 1) r 3 r 3 dr 3 = - a r 3 dt + Ρdz (8) r 3, r 3 r 3 = 0 r 3 t, r r= Ρ 3 t, t (i, j ) t= i t, r 3 = j r Α> 0, j (jm ax) (jm in), p u, p m p d H u ll W h ite, jm ax g(Α t), jm ax= - jm in, r= Ρ 3 t, p u = a j t - a j t, p m = 3 - a j t p d = a j t + a j t g p u = a j t - a j t, p m = - p d = a j t + 3a j t a j t - a j t p u = a j t - 3a j t, p m = a j t + a j t (9) (10)

5 8 59 ) r p d = a j t - a j t, r 3 r bi r i t r r 3 i t r 3 B (i, j) (i, j ) (0, 0) r r 3 bi bi, (0, 0), b0 t t b0 : b0= R ( t), R ( t) t B (1, 1), B (1, 0) B (1, - 1) B (1, 1) = p u (0, 0) e - b 0, B (1, 0) = p m (0, 0) e - b 0, B (1, - 1) = p d (0, 0) e - b 0 (1) p u (0, 0), p m (0, 0) p d (0, 0) (0, 0) B (1, 1), B (1, 0) B (1, - 1) b1 B (1, 1) e - (b 1 + r) + B (1, 0) e - b 1 + B (1, - 1) e - (b 1 - r) = e - R ( t)g t (13) R ( t) t B (, ), B (, 1), B (, 0), B (, - 1) B (, - ) B (1, 1), B (1, 0) B (1, - 1), (1, 1), (1, 0) (1, - 1) b1- r, b1 b1+ r, (1) 3 t R (3 t) (13) b bi r 4., V C ic CS (callab le secu rity),, 1 V C ic V C (1+ ic) N CS (noncallab le secu rity) 0 (11) N CS 0 = [E (N CS 1) + V C ic) ]g(1 + r (0, 0) ) (14) r (0, 0) (0, 0), E (N CS 1) N CS 1 E (N CS 1) = N CS (1, 1) p u (0, 0) + N CS (1, 0) p m (0, 0) + N CS (1, - 1) p d (0, 0) (15) N CS (1, 1), N CS (1, 0) N CS (1, - 1) N CS (1, 1), (1, 0) (1, - 1), CO (callab le op tion) 0 E (CO 1) CO 1 CO 0 = m ax [ (N CS 0 - V C), E (CO 1) g(1 + r (0, 0) ] (16) E (CO 1) = CO (1, 1) p u (0, 0) + CO (1, 0) p m (0, 0) + CO (1, - 1) p d (0, 0) (17) CO (1, 1), CO (1, 0) CO (1, - 1) (1, 1), (1, 0) (1, - 1), CS 0 CS 0 = N CS 0 - CO 0 (18),, N CS, CO CS, CO 1 N CS CS 1 CO (1, j) = m ax [N CS (1, j) - V c, 0 ], J = - 1, 0, 1 (19) N CS (1, j) = V c (1 + ic) g(1 + r (1, j) ),, J = - 1, 0, 1 (0) CS (1, j) = N CS (1, j) - CO (1, j),, J = - 1, 0, 1 (1),

6 : [1 ],. [J ]., 1998, (1): [ ]. [M ]. :, 1999, [3 ] H ull J, W h ite A. O ne facto r interest rate models and the valuation of interest rate derivative securities[j ]. Journal of F inancial and Q uan titative A nalysis, 1993, 8: [4 ] H ull J, W h ite A. N um erical p rocedure fo r imp lem enting term structure models: singlefacto r models[j ]. Journal of D erivatives, 1994, Fall: ( 40 ), (15) : [1 ] B rennan M J, Schw artz E S. Convertible bonds: valuation and op tim al strategies fo r call and conversion [J ]. T he Jou rnal of F inance, 1977, 7 (5): [ ] B rennan M J, Schw artz E S. A nalyzing convertible bonds[j ]. Journal of F inancial and Q uantitative A nalysis, 1980, 15 (4): [3 ] Evnine J J. T h ree essays in the use of op tion p ricing theo ry[d ]. Berkeley: U niversity of Califo rnia, [4 ] H arrison J M, P liska S R. M artingales and stochastic integrals in the theo ry of continuous trading [J ]. Stochastic P rocesses and T heir A pp lication s, 1981, 11: [5 ] H eath D, Jarrow R, M o rton A. Bond p ricing and the term structure of interest rates: a new m ethodo logy fo r contin gen t claim s valuation[j ]. Econom etrica, 199, 60 (1): [6 ] Ho T S Y, L ee S B. T erm structure movem ents and p ricing interest rate contingent claim s[j ]. T he Journal of F i nance, 1986, 41 (5): [7 ] Ingerso ll, J r, J E. A ContingentC laim s valuation of convertible securities [J ]. Journal of F inancial Econom ics, 1977a, 13 (4): [8 ] Johnson H. Op tions on the m axim um o r the m inim um of several assets[j ]. Journal of F inancial and Q uantitative A nalysis, 1987, (3): [9 ]. [M ]. :, [10 ]. [N ].,

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