外国為替市場におけるモーメント・リスクプレミアムに関する考察

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2 5 =

3 X E P t [X m t+1 ] EQ t [X m t+1 ]

4 (2015) Recover 1 ( ) 2 Carr and Wu(2009) Kozhan, Neuberger, and Schneider(2013) ( ) 2 3 Della Corte, Ramadorai, and Sarno(2014) Huang and Mac- Donald(2015) ( USD) ( Theorem) Audrino, Huitema, and Ludwig (2014) ( USD JPY) 4 -

5 (1/2) θ 0 θ T ψ(θ T θ 0 ) 1 0 payoff v 0 = g(θ T )ψ(θ T θ 0 )dθ T e r(θ 0)T = ψ(θ T θ 0 )dθ T *g(θ T ) payoff 1 π (θ T θ 0 ) ψ(θ T θ 0 ) ψ(θt θ 0 )dθ T = e r(θ 0)T ψ(θ T θ 0 )

6 (2/2) ( ) v 0 = e r(θ 0)T g(θ T )π (θ T θ 0 )dθ T e r(θ 0)T E Q [g(θ T )] π(θ T θ 0 ) ( ) [ v 0 = e r(θ0)t E P g(θ T ) π (θ T θ 0 ) π(θ T θ 0 ) ] = E P [ ] g(θ T ) ψ(θ T θ 0 ) π(θ T θ 0 ) ψ(θ T θ 0 ) π(θ T θ 0 ) ϕ(θ T θ 0 ) payoff = Recover

7 .1 smile.2 call.3.4 (time homogeneous) 1 spot 1 spot.5 Teorem.6

8 JPY USD EUR NOK SEK AUD NZD CHF GBP CAD JPY USD 9 spot forward OP forward OP 1M 2M 3M 2004/1-2015/10 NY Bloomberg

9 USD/JPY

10 OP informed / JPY 9 USD 9 JPY USD () NY TTM ( 10 )

11 CRP CRP VRP VRP SRP SRP KRP KRP 4

12 1-4 (Ratio) Mean S.E. Stdev Ratio Skew correlation matrix vs JPY CRP VRP SRP KRP CRP VRP SRP KRP ** vs USD CRP VRP SRP KRP CRP VRP ** SRP KRP * *** * 10% ** 5% *** 1%

13 Carry(CAR) Brunnermeier, Nagel, and Pedersen(2008) Risk-Reversal(RR) 10 Risk-Reversal ( ) Farhi et al.(2013) Della Corte, Ramadorai, and Sarno(2014) Momentum(MOM) 3 Della Corte, Ramadorai, and Sarno(2014) Menkhoff et al.(2012) Value(VAL) 5 ( ) Asness, Clifford, and Pedersen(2013) Raza(2015)

14 Mean S.E. Stdev Ratio Skew correlation matrix vs JPY CAR RR MOM VAL CAR RR MOM VAL ** vs USD CAR RR MOM VAL CAR RR MOM VAL *** * 10% ** 5% *** 1%

15 USD =

16 () (2015) Theorem 10 JPY USD 9 MPR

18 Theorem (1/4) 1 ψ(θ t+1 θ t ) = ϕ(θ t+1 θ t )π(θ t+1 θ t ). (1) ϕ ϕ(θ t+1 θ t ) = δ h(θ t+1) h(θ t ), (2) δ h

19 Theorem (2/4) (2) (1) ψ(θ t+1 θ t ) = δ h(θ t+1) h(θ t ) π(θ t+1 θ t ). (3) θ t = 1, 2,, s,, S DΨ = δπd, (4) Ψ Π D

20 Theorem (3/4) (4) Π ( ) 1 Π = DΨD 1. (5) δ Π 1 1 (S 1) e Πe = e, (6) (5) e ( ) 1 Πe = DΨD 1 e = e. δ

21 Theorem (4/4) ΨD 1 e = δd 1 e. z D 1 e, (7) Ψz = δz, (8) Ψ Ψ ( ) Perron Frobenius

22 (1/2) OP At-The-Money(ATM) IV(σ ATM ) 10delta Risk-Reversal(RR 10 ) 25delta Risk-Reversal (RR 25 ) 10delta Butterfly(BF 10 ) 25delta Butterfly (BF 25 ) IV RR BF ATM Out-of-The-Money(OTM) call put IV RR = σ OTMcall σ OTMput, BF = 0.5strangle straddle = 0.5(σ OTMcall + σ OTMput ) σ ATM.

23 (2/2) 4 IV σ ATM 5 IV σ call10 = σ ATM + 0.5RR 10 + BF 10, σ put10 = σ ATM 0.5RR 10 + BF 10, σ call25 = σ ATM + 0.5RR 25 + BF 25, σ put25 = σ ATM 0.5RR 25 + BF 25.

24 (1/4).1 smile 5 IV smile Malz(2014) ( ) cubic spline Deep-OTM IV -IV smile -IV smile ( -IV smile ).2 call Clark(2011).3 Breeden and Litzenberger(1978) 2 call C(t, τ, K s ) 1 (C(t, τ, K ) 2C(t, τ, K) + C(t, τ, K + )).

25 (2/4).4 Ψ Backwell(2015) min 0 ψ(θ t+1 =s t+1 θ t =s t ) 1 g(ψ) + h(ψ), s.t. 0 s t+1 ψ(θ t+1 = s t+1 θ t = s t ) 2. g(ψ) = τ h(ψ) = s t (ψ t,τ+1 ψ t,τ Ψ )( ψ t,τ+1 ψ t,τ Ψ ), ( ψ(θ t+1 = s t+1 1 θ t = s t) 2ψ(θ t+1 = s t+1 θ t = s t) s t+1 + ψ(θ t+1 = s t θ t = s t)) 2.

26 (3/4).5 Teorem Ψ = (8) = ϕ δ (5) = Π Recover = 1-4 π k r s π s r s µ, π s (r s µ) 2 σ 2, Mean = s Skew = s Var = s π s (r s µ) 3 σ 3, Kurt = s π s (r s µ) 4 σ 4.

27 (4/4).6 1 = πk 3 ψ(θ t+τ = s θ t ) π s = ψ(θ t+1 = s θ t ) s ψ(θ t+1 = s θ t ). 5

28 I Asness, C. S., T. J. Moskowitz, and L. H. Pedersen (2013). Value and momentum everywhere. The Journal of Finance 68(3), Audrino, F., R. Huitema, and M. Ludwig (2014). An empirical analysis of the ross recovery theorem. Available at SSRN Backwell, A. (2015). State prices and implementation of the recovery theorem. Journal of Risk and Financial Management 8(1), Bakshi, G. and N. Kapadia (2003). Delta-hedged gains and the negative market volatility risk premium. Review of Financial Studies 16(2), Bank for International Settlements (2015). Triennial central bank survey foreign exchange turnover in april 2013:preliminary global results. Black, F. (1976). The pricing of commodity contracts. Journal of financial economics 3(1), Black, F. and M. Scholes (1973). The pricing of options and corporate liabilities. The journal of political economy, Bollerslev, T., G. Tauchen, and H. Zhou (2009). Expected stock returns and variance risk premia. Review of Financial Studies 22(11),

29 II Borovička, J., L. P. Hansen, and J. A. Scheinkman (2014). Misspecified recovery. NBER Working Paper (w20209). Breeden, D. T. and R. H. Litzenberger (1978). Prices of state-contingent claims implicit in option prices. Journal of business, Britten-Jones, M. and A. Neuberger (2000). Option prices, implied price processes, and stochastic volatility. The Journal of Finance 55(2), Brunnermeier, M. K., S. Nagel, and L. H. Pedersen (2008). Carry trades and currency crashes. Technical report, National Bureau of Economic Research. Carr, P. and L. Wu (2009). Variance risk premiums. Review of Financial Studies 22(3), Carr, P. and J. Yu (2012). Risk, return, and ross recovery. Journal of Derivatives 20(1), 38. Christoffersen, P., M. Fournier, K. Jacobs, and M. Karoui (2015). Option-based estimation of the price of co-skewness and co-kurtosis risk. Available at SSRN

30 III Clark, I. J. (2011). Foreign exchange option pricing: A practitioners guide. John Wiley & Sons. Della Corte, P., T. Ramadorai, and L. Sarno (2014). Volatility risk premia and exchange rate predictability. Available at SSRN Dubynskiy, S. and R. S. Goldstein (2013). Recovering drifts and preference parameters from financial derivatives. Available at SSRN Fama, E. F. (1984). Forward and spot exchange rates. Journal of Monetary Economics 14(3), Garman, M. B. and S. W. Kohlhagen (1983). Foreign currency option values. Journal of international Money and Finance 2(3), Hansen, L. P. and J. A. Scheinkman (2009). Long-term risk: An operator approach. Econometrica 77(1), Huang, H., R. MacDonald, and Y. Zhao (2013). Global currency misalignments, crash sensitivity, and moment risk premia. In 2015 American Economic Association Annual Meeting.

31 IV Jensen, C. S., D. Lando, and L. H. Pedersen (2015). Generalized recovery. Available at SSRN Jordà, Ò. and A. M. Taylor (2012). The carry trade and fundamentals: nothing to fear but feer itself. Journal of International Economics 88(1), Kozhan, R., A. Neuberger, and P. Schneider (2013). The skew risk premium in the equity index market. Review of Financial Studies 26(9), Liu, F. (2014). Recovering conditional return distributions by regression: Estimation and applications. Available at SSRN Londono, J. M. and H. Zhou (2014). Variance risk premiums and the forward premium puzzle. Available at SSRN Malz, A. M. (2014). A simple and reliable way to compute option-based risk-neutral distributions. FRB of New York Staff Report (677). Martin, I. and S. A. (2013). The long bond. Technical report, Working Paper, Stanford University.

32 V Meese, R. A. and K. Rogoff (1983). Empirical exchange rate models of the seventies: Do they fit out of sample? Journal of international economics 14(1), Mehra, R. and E. C. Prescott (1985). The equity premium: A puzzle. Journal of monetary Economics 15(2), Menkhoff, L., L. Sarno, M. Schmeling, and A. Schrimpf (2012). Currency momentum strategies. Journal of Financial Economics 106(3), Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, Neuberger, A. (2012). Realized skewness. Review of Financial Studies 25(11), Park, H. (2014). recovery with recurrent and transient processes. arxiv preprint arxiv: Qin, L. and V. Linetsky (2014). recovery in continuous time. Available at SSRN

33 VI Raza, A. (2015). Currency value strategies. Available at SSRN , S. (2015). The recovery theorem. The Journal of Finance 70(2), , S. A. (2011). The recovery theorem. NBER Working Paper (w17323). Sasaki, H. (2014). Essays on risk premiums in higher-order moments of financial asset returns. Spears, T. (2013). On estimating the risk-neutral and real-world probability measures. Ph. D. thesis, Oxford University. Tsui, H. M. (2013). recovery theorem and its extension. Mathematical Finance. Walden, J. (2014). with unbounded diffusion processes. Available at SSRN Yaron, A. and R. Bansal (2004). Risks for the long run: A potential resolution of asset pricing puzzles. The Journal of finance 59(4),

2 Recovery Theorem Spears [2013]Audrino et al. [2015]Backwell [2015] Spears [2013] Ross [2015] Audrino et al. [2015] Recovery Theorem Tikhonov (Tikhon

2 Recovery Theorem Spears [2013]Audrino et al. [2015]Backwell [2015] Spears [2013] Ross [2015] Audrino et al. [2015] Recovery Theorem Tikhonov (Tikhon Recovery Theorem Forward Looking Recovery Theorem Ross [2015] forward looking Audrino et al. [2015] Tikhonov Tikhonov 1. Tikhonov 2. Tikhonov 3. 3 1 forward looking *1 Recovery Theorem Ross [2015] forward

外国為替市場における モーメント・リスクプレミアムに関する考察

外国為替市場におけるモーメント・リスクプレミアムに関する考察