Article Contents
Article Contents

# Lower and upper pricing of financial assets

• Mathematics Subject Classification: G10, G12, G13.

 Citation:

• Table 1.  Moment transforms of bilateral gamma parameter estimates

 Quantile d v s k 1 −0.0038 0.0070 −0.9097 3.0281 5 −0.0016 0.0084 −0.6409 3.2262 10 −0.0007 0.0093 −0.4789 3.4830 25 0.0004 0.0115 −0.1229 3.9540 50 0.0012 0.0150 0.0418 4.5340 75 0.0017 0.0209 0.1493 5.1621 90 0.0023 0.0305 0.2635 5.8350 95 0.0027 0.0408 0.3535 6.3046 99 0.0038 0.0707 0.5982 7.4617

Table 2.  Lower and upper return quantiles

 Quantile Lower Upper $1$ $-0.0540$ $-0.0479$ $5$ $-0.0267$ $-0.0227$ $10$ $-0.0167$ $-0.0146$ $25$ $-0.0053$ $-0.0056$ $50$ $0.0020$ $0.0010$ $75$ $0.0083$ $0.0070$ $90$ $0.0167$ $0.0151$ $95$ $0.0237$ $0.0223$ $99$ $0.0458$ $0.0480$

Table 3.  SPY states

 State $b_{p}$ $c_{p}$ $b_{n}$ $c_{n}$ $1$ $0.0054$ $1.2937$ $0.0097$ $0.6195$ $2$ $0.0057$ $1.2603$ $0.0059$ $1.0112$ $3$ $0.0053$ $1.3110$ $0.0077$ $0.7423$ $4$ $0.0034$ $2.3575$ $0.0049$ $1.3701$ $5$ $0.0061$ $1.1068$ $0.0085$ $0.6450$ $6$ $0.0042$ $1.7842$ $0.0059$ $1.0625$ $7$ $0.0058$ $1.2971$ $0.0077$ $0.8604$ $8$ $0.0011$ $12.049$ $0.0028$ $4.4096$

Table 4.  Measure distortion parameters for the myopic case

 $b$ $c$ $2017$ $8.1711$ $863.3857$ $t{\text{-}}stat$ $(3.62)$ $(3.12)$ $2018$ $1.6311$ $78.1643$ $t{\text{-}}stat$ $(16.31)$ $(13.13)$ $2019$ $1.8594$ $85.7347$ $t{\text{-}}stat$ $(16.36)$ $(13.25)$

Table 5.  Measure distortion parameters for the Markov modulated case

 $b$ $c$ $2017$ $0.008962$ $0.475662$ $t{\text{-}}stat$ $(30.04)$ $(12.79)$ $2018$ $0.039580$ $0.500025$ $t{\text{-}}stat$ $(109.82)$ $(47.43)$ $2019$ $0.014905$ $0.469397$ $t{\text{-}}stat$ $(48.38)$ $(20.64)$

Table 6.  Maximal risk charges

 Modulated No Modulation $2017$ $0.01884$ $0.00946$ $2018$ $0.07916$ $0.02087$ $2019$ $0.03175$ $0.02169$

Tables(6)