The Information Hidden in Derivatives Markets
Emlyn Flint – Peregrine Securities
(With Anthony Seymour & Florence Chikurunhe at Peregrine
Securities and Eben Maré at University of Pretoria)
Actuarial Society 2016 Convention 23 – 24 November 2016
Contents
1. Motivation
2. Estimating Implied Distributions
3. Ross Recovery Theorem
4. Top40 Index Option Results
5. Conclusion
Actuarial Society 2016 Convention 23 – 24 November 2016
Actuarial Society 2016 Convention 23 – 24 November 2016
Theory vs. Reality
Black-Scholes-Merton
Reality
Actuarial Society 2016 Convention 23 – 24 November 2016
Motivation
Theory vs. Reality
Reality
Top40 Volatility Surface - 18 Sep 2006
0.4
Volatility
0.35
0.3
0.25
0.2
80
100
120
Strike
?
⟺
0.25
0.5
0.75
1
1.25
1.5
Term
Actuarial Society 2016 Convention 23 – 24 November 2016
Implied Information
1 Portfolio Management
• Expected Return & Volatility estimates
• Average Implied Correlation (CIX)
• Forward-looking Implied Betas
• Tactical Asset Allocation
2 Risk Management
• Forward-looking Volatility estimates (VIX & SKEW)
• Forward-looking Implied VaR
• Regime Identification
Actuarial Society 2016 Convention 23 – 24 November 2016
Contents
1. Motivation
2. Estimating Implied Distributions
3. Ross Recovery Theorem
4. Top40 Index Option Results
5. Conclusion
Actuarial Society 2016 Convention 23 – 24 November 2016
Actuarial Society 2016 Convention 23 – 24 November 2016
Breeden-Litzenberger (1978)
Option
Value:
Strike
Delta:
Strike
Gamma:
∞
𝐶 𝐾, 𝑇 = 𝑒 −𝑟𝑇
0
𝜕𝐶
𝑟𝑇
𝑒
=−
𝜕𝐾
𝑆𝑇 − 𝐾
+
𝑞 𝑆 𝑑𝑆
Q
∞
𝑞 𝑆 𝑑𝑆
𝐾
2𝐶
𝜕
𝑒 𝑟𝑇
=𝑞 𝐾
2
𝜕𝐾
Option-Implied Risk-Neutral
Distribution (RND)
Actuarial Society 2016 Convention 23 – 24 November 2016
Implied Information
1 Direct Estimation from Expectation Integral
• Complex underlying distributions or expansion terms
• Mixture of lognormals
• Entropy-based methods
• Kernel Smoothing
2 Indirect Estimation from Implied Volatility Skews
• Cubic splines for interpolation and extrapolation
• Deterministic volatility models (SVI, quadratic)
• Stochastic volatility models (Heston, SABR)
• Jump Diffusion Processes (Merton)
Actuarial Society 2016 Convention 23 – 24 November 2016
Implied Information
1 Direct Estimation from Expectation Integral
• Complex underlying distributions or expansion terms
• Mixture of lognormals
• Entropy-based methods
• Kernel Smoothing
2 Indirect Estimation from Implied Volatility Skews
• Cubic splines for interpolation and extrapolation
• Deterministic volatility models (SVI, quadratic)
• Stochastic volatility models (Heston, SABR)
• Jump Diffusion Processes (Merton)
Actuarial Society 2016 Convention 23 – 24 November 2016
Calculating the RND
1
Calibrate the SVI Model
Actuarial Society 2016 Convention 23 – 24 November 2016
Calculating the RND
1
Calibrate the SVI Model
Actuarial Society 2016 Convention 23 – 24 November 2016
Calculating the RND
2
Convert to BS Call Prices
Actuarial Society 2016 Convention 23 – 24 November 2016
Calculating the RND
3
Use Breeden-Litzenberger
Actuarial Society 2016 Convention 23 – 24 November 2016
Estimating Implied Distributions
Calculating the RND
1
2
3
Actuarial Society 2016 Convention 23 – 24 November 2016
An RND Surface
RNDs are NOT equivalent to
Real-world distributions!
Actuarial Society 2016 Convention 23 – 24 November 2016
Actuarial Society 2016 Convention 23 – 24 November 2016
Contents
1. Motivation
2. Estimating Implied Distributions
3. Ross Recovery Theorem
4. Top40 Index Option Results
5. Conclusion
Actuarial Society 2016 Convention 23 – 24 November 2016
Actuarial Society 2016 Convention 23 – 24 November 2016
Ross Recovery Theorem
Risk-Neutral
Real-World
𝑷 = 𝝍𝑭
Ross (2015) Recovery Theorem can extract pricing kernel and realworld probabilities simultaneously
RECOVERY ASSUMPTIONS
1. Markets are complete and arbitrage-free
2. The underlying takes on a finite number of states
Actuarial Society 2016 Convention 23 – 24 November 2016
Ross Recovery Theorem
Risk-Neutral
Real-World
𝑷 = 𝝍𝑭
Ross (2015) Recovery Theorem can extract pricing kernel and realworld probabilities simultaneously
RECOVERY ASSUMPTIONS
1. Markets are complete and arbitrage-free
2. The underlying takes on a finite number of states
3. The transition probability matrix (TPM) is
irreducible and time-independent
Actuarial Society 2016 Convention 23 – 24 November 2016
Ross Recovery Theorem
Risk-Neutral
Real-World
𝑷 = 𝝍𝑭
Ross (2015) Recovery Theorem can extract pricing kernel and realworld probabilities simultaneously
RECOVERY ASSUMPTIONS
1. Markets are complete and arbitrage-free
2. The underlying takes on a finite number of states
3. The transition probability matrix (TPM) is
irreducible and time-independent
4. The pricing kernel is path-independent
Actuarial Society 2016 Convention 23 – 24 November 2016
Ross Recovery Theorem
For those interested in the maths…
𝑝𝑖𝑗
𝐷𝑒𝑓𝑖𝑛𝑒 𝜓𝑖𝑗 =
.
𝑓𝑖𝑗
𝐹𝑟𝑜𝑚 𝐴2 & 𝐴3 ⟹ 𝑃𝒛 = 𝜆𝒛.
letting 𝐻 = 𝑑𝑖𝑎𝑔 ℎ 𝑆1 , … , ℎ(𝑆𝑛 ) :
ℎ(𝑆𝑗 )
𝐹𝑟𝑜𝑚 𝐴4 ⟹ 𝜓𝑖𝑗 = 𝛿
ℎ(𝑆𝑖 )
𝑃 = 𝛿𝐻 −1 𝐹𝐻 ⟺ 𝐹 = 𝐻𝑃𝐻 −1 .
𝛿
1
𝐵𝑢𝑡 𝟏 = 𝐹𝟏 = 𝐻𝑃𝐻−1 𝟏,
𝛿
∴ 𝑃𝐻 −1 𝟏 = 𝛿𝐻 −1 𝟏 ⟹ 𝒛 = 𝐻 −1 𝟏.
ℎ(𝑆𝑗 )
∴ 𝑝𝑖𝑗 = 𝛿
𝑓 .
ℎ(𝑆𝑖 ) 𝑖𝑗
1
Actuarial Society 2016 Convention 23 – 24 November 2016
Applying the Recovery Theorem
1
Market Prices

2
RND

3
TPM

4
Real-World
Actuarial Society 2016 Convention 23 – 24 November 2016
Applying the Recovery Theorem
1
Market Prices

2
RND

3
TPM

4
Real-World
Actuarial Society 2016 Convention 23 – 24 November 2016
Applying the Recovery Theorem
1
Market Prices

2
RND

3
TPM

4
Real-World
Actuarial Society 2016 Convention 23 – 24 November 2016
Applying the Recovery Theorem
Density
1
Market Prices
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

2
RND

3
TPM

4
Real-World
Risk-Neutral, μ = 8.7%
Real-World, μ = 14.7%
50
60
70
80
90
100
110
Spot Moneyness
120
130
140
150
Actuarial Society 2016 Convention 23 – 24 November 2016
Contents
1. Motivation
2. Estimating Implied Distributions
3. Ross Recovery Theorem
4. Top40 Index Option Results
5. Conclusion
Actuarial Society 2016 Convention 23 – 24 November 2016
Actuarial Society 2016 Convention 23 – 24 November 2016
South African Recovery
Volatility Surface Data
• SAFEX trades from Sep 2005 – Jan 2016
• SVI volatility skews for each SAFEX expiry
• Strike extrapolation for 20 – 300% Moneyness
• Term interpolation & Extrapolation: [1, 24] months
Focus of Analysis
• Weekly RND Surfaces
• Recovered 3-month Real-World Distributions
• Expected Return, Volatility, Skewness & Kurtosis
• Tactical Asset Allocation with Implied Moments
Actuarial Society 2016 Convention 23 – 24 November 2016
History of 3-Month RND’s
150
140
95th
Spot Moneyness
130
120
110
50th
75th
100
25th
90
80
70
5th = Implied VaR
60
50
Sep-05
Sep-07
Sep-09
Sep-11
Sep-13
Sep-15
Actuarial Society 2016 Convention 23 – 24 November 2016
Full RND at 1 Feb 2016
150
Spot Moneyness
Distribution
130
95th
Median
110
90
70
5th
50
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14
Future time, in months
Actuarial Society 2016 Convention 23 – 24 November 2016
RND vs. Real-World Moments
Expected Return, %
30
20
10
0
Sep-05
Sep-07
Sep-09
Sep-11
Sep-13
Sep-15
Volatility, %
60
40
20
0
Sep-05
Sep-07
Sep-09
ActuarialSep-11
Society 2016 Convention
23 – 24 November
2016
Sep-13
Sep-15
RND vs. Real-World Moments
Skewness
1
0
-1
-2
Sep-05
Sep-07
Sep-09
Sep-11
Sep-13
Sep-15
Kurtosis
15
10
5
0
Sep-05
Sep-07
Sep-09
Actuarial
Society 2016 Convention
2016
Sep-11
Sep-13 23 – 24 November
Sep-15
TAA with Implied Moments
SIMPLE TIMING STRATEGY
•
•
•
•
Four independent moment timing strategies
If current week’s exp. return, skewness or kurtosis is higher
than previous week then hold Top40, otherwise hold cash
If current week’s volatility is lower than previous week then
hold Top40, otherwise hold cash
No costs included
Actuarial Society 2016 Convention 23 – 24 November 2016
Cumulative Log-Return
TAA with Implied Moments
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
Sep-05
RN Mean
RN Skew
RW Mean
RW Skew
RN Vol
RN Kurt
RW Vol
RW Kurt
Real-World
Risk-Neutral
Sep-07
Sep-09
Sep-11
Sep-13
Sep-15
Actuarial Society 2016 Convention 23 – 24 November 2016
TAA with Implied Moments
Actuarial Society 2016 Convention 23 – 24 November 2016
TAA with Implied Moments
Real-world TAA strategies dominate Top40 mean and volatility
Actuarial Society 2016 Convention 23 – 24 November 2016
TAA with Implied Moments
Real-world TAA strategies dominate Top40 mean and volatility
RN Skewness is the only RN moment showing good performance
Actuarial Society 2016 Convention 23 – 24 November 2016
TAA with Implied Moments
Real-world TAA strategies dominate Top40 mean and volatility
RN Skewness is the only RN moment showing good performance
Simple TAA strategies still show high drawdown
Actuarial Society 2016 Convention 23 – 24 November 2016
Contents
1. Motivation
2. Estimating Implied Distributions
3. Ross Recovery Theorem
4. Top40 Index Option Results
5. Conclusion
Actuarial Society 2016 Convention 23 – 24 November 2016
Vol Surface is a Forecasting Tool
Actuarial Society 2016 Convention 23 – 24 November 2016
Estimating Implied Distributions
Estimate the Implied RN Distribuion
1
2
3
Actuarial Society 2016 Convention 23 – 24 November 2016
Apply the Recovery Theorem
Density
1
Market Prices
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

2
RND

3
TPM

4
Real-World
Risk-Neutral, μ = 8.7%
Real-World, μ = 14.7%
50
60
70
80
90
100
110
Spot Moneyness
120
130
140
150
Actuarial Society 2016 Convention 23 – 24 November 2016
Use the Implied Information
1 Portfolio Management
• Expected Return & Volatility estimates
• Average Implied Correlation (CIX)
• Forward-looking Implied Betas
• Tactical Asset Allocation
2 Risk Management
• Forward-looking Volatility estimates (VIX & SKEW)
• Forward-looking Implied VaR
• Regime Identification
Actuarial Society 2016 Convention 23 – 24 November 2016
Thank You
Questions?
Actuarial Society 2016 Convention 23 – 24 November 2016